- Start measuring where the rays meet. - Make sure the protractor's zero line follows one ray. - After measuring, compare the angle with a right angle.

1. Place the protractor's center at \(K\) and line up the starting edge with ray \(KM\). 2. The other ray passes through the \(60^\circ\) mark. 3. Since \(60^\circ\) is less than \(90^\circ\), the angle is acute.

\(60^\circ\); acute.

- Find the common starting point of the two rays. - Choose the protractor scale whose zero follows one of the rays. - Check whether the result is larger or smaller than a right angle.

1. The rays start together at \(S\). Put the protractor's center there. 2. The opening between the rays measures \(120^\circ\). 3. An angle greater than \(90^\circ\) but less than \(180^\circ\) is obtuse.

\(120^\circ\); obtuse.

- The vertex of the angle is \(B\). - Align the protractor with one side of the angle before reading the scale. - Check that your answer matches the acute appearance of the angle.

1. Place the protractor's center at \(B\). 2. Align the baseline with ray \(BA\). 3. Ray \(BC\) crosses the correct scale at \(42^\circ\).

\(42^\circ\)

- Place the center mark of the protractor at \(V\). - Align the zero line with ray \(a\). - Read the scale that starts at zero on ray \(a\).

1. Center the protractor at \(V\) and align its baseline with ray \(a\). 2. Ray \(b\) meets the correct scale at \(64^\circ\).

\(64^\circ\)

- Put the center mark of the protractor at the angle's vertex. - Align the zero line with one ray before reading the other ray. - Choose the scale that starts at zero on the aligned ray.

1. Place the protractor's center at \(O\) and align its baseline with ray \(a\). 2. Read the scale where ray \(b\) crosses it. 3. The smaller angle measures \(35^\circ\).

\(35^\circ\)

- Look for a point shared by both drawn arms. - The angle opens out from one point.

1. The two sides of the pictured angle meet at B. 2. Place the protractor's center at B, the vertex of the angle.

At B, where the two arms meet.

- Look at the direction of each arm from P, not just the location of its endpoint. - Imagine laying a straight ruler along the stated zero line.

1. PA is the horizontal arm pointing right. 2. It matches the protractor's right-pointing zero line.

PA.

- The boards form an obtuse angle. - Rotate the protractor so one baseline follows one board. - Use the scale that starts at \(0^\circ\) on the aligned board.

1. Center the protractor at \(P\). 2. Align a baseline with either board. 3. The smaller angle measures \(118^\circ\).

\(118^\circ\)

- Measure the opening at the joint before checking the interval. - Use the smaller angle formed by the two arms. - Compare your measurement with both endpoints of the stated range.

1. Measure the angle between the two arms at \(J\). 2. The opening measures \(103^\circ\). 3. Since \(103^\circ\) is between \(95^\circ\) and \(110^\circ\), it meets the stated exercise rule.

\(103^\circ\); yes, it meets the stated rule.

- The baseline of the protractor does not have to be horizontal. - Align the zero line with ray \(a\), even though that ray is tilted. - Read the scale that increases away from the zero on ray \(a\).

1. Center the protractor at \(V\) and rotate it so its baseline follows ray \(a\). 2. Use the scale that begins at zero on ray \(a\). 3. Ray \(b\) meets that scale at \(75^\circ\).

\(75^\circ\)

- The baseline is tilted, so the page's horizontal direction is not the protractor's zero line. - Align the protractor with one of the rays rather than with the edge of the page. - Check whether your reading should be acute or obtuse from the visible opening.

1. Center the protractor at \(O\) and align its baseline with either ray. 2. Read from the zero that lies on the aligned ray. 3. The rays are \(120^\circ\) apart, so the smaller angle measures \(120^\circ\).

\(120^\circ\)

- Decide which ray should line up with zero before reading a number. - A standard protractor often shows two numbers at the same tick. - Use the visible size of the smaller angle to test which reading is reasonable.

1. Align the protractor's baseline with ray \(a\) and start from the zero on that ray. 2. Ray \(b\) gives a reading of \(65^\circ\) on the correct scale. 3. Lena used the opposite scale, so \(115^\circ\) is not the smaller angle.

No. The smaller angle is \(65^\circ\); Lena read the opposite protractor scale.

- Treat ray \(s\) as the protractor's zero direction. - Measure each candidate from the same starting ray. - Select the ray whose measurement matches the requested angle.

1. Align the protractor's zero line with ray \(s\). 2. Ray \(a\) is at \(70^\circ\), ray \(b\) is at \(62^\circ\), and ray \(c\) is at \(78^\circ\) from ray \(s\). 3. Therefore ray \(a\) forms the requested \(70^\circ\) angle.

Ray \(a\)

- Look at where the two rows of numbers begin and end. - What does each short mark between printed numbers stand for?

1. The right-pointing horizontal arm lies at \(0^\circ\) on the outer scale. 2. The slanted arm reaches the second small mark after \(90^\circ\) on that scale, giving \(110^\circ\).

\(110^\circ\)

- Imagine measuring a small turn from each end of the protractor. Would both readings be the same? - What do the short marks mean between the printed numbers?

1. The left-pointing horizontal arm lies at \(0^\circ\) on the inner scale. 2. The slanted arm reaches the next small mark after \(30^\circ\) on that scale, giving \(40^\circ\).

\(40^\circ\), because the left-zero scale matches the starting arm.

- Find where the two straight arms meet. - Compare that point with the protractor's center mark.

1. The two straight arms meet at P, but the center mark is at Q. 2. Move the protractor until its center is at P before measuring.

No. Move the protractor's center from Q to P.

- Measure the named vertex angle in each panel separately. - Do not compare the drawings by appearance alone. - After measuring, subtract the smaller angle from the larger one.

1. In figure a), the angle at \(A\) measures \(67^\circ\). 2. In figure b), the angle at \(P\) measures \(104^\circ\). 3. Figure b) has the greater angle. 4. The difference is \(104^\circ - 67^\circ = 37^\circ\).

Figure b), by \(37^\circ\).

- Measure the acute angle, not the obtuse angle beside it. - Keep the protractor's center exactly at the crossing point. - Compare your measured value with Jordan's recorded value.

1. Center the protractor at the intersection point and align its baseline with either path. 2. The acute angle measures \(58^\circ\). 3. Jordan's measurement is \(58^\circ - 52^\circ = 6^\circ\) too small.

No. The acute angle is \(58^\circ\), so Jordan's measurement is \(6^\circ\) too small.

- Measure the two smaller adjacent angles first. - Keep the protractor centered at \(V\) each time. - Add the two measured angles before checking the whole angle directly.

1. The angle between rays \(a\) and \(b\) measures \(36^\circ\). 2. The angle between rays \(b\) and \(c\) measures \(53^\circ\). 3. Their sum is \(36^\circ+53^\circ=89^\circ\). 4. A direct measurement of the angle between rays \(a\) and \(c\) also gives \(89^\circ\).

The angle between rays \(a\) and \(b\) is \(36^\circ\), the angle between rays \(b\) and \(c\) is \(53^\circ\), and the angle between rays \(a\) and \(c\) is \(89^\circ\).

- Measure the smaller opening between the two rays, even though it is close to a straight angle. - Check that you are reading from the scale whose zero is aligned with ray \(a\). - After measuring, compare the angle with the degree measure of a straight angle.

1. The smaller angle between the rays measures \(153^\circ\). 2. A straight angle measures \(180^\circ\). 3. The difference is \(180^\circ-153^\circ=27^\circ\).

The angle is \(153^\circ\), which is \(27^\circ\) less than a straight angle.

- Measure each panel independently before comparing the angles. - For each angle, align the protractor with one ray and read from the matching zero. - After measuring both, subtract the smaller measure from the larger one.

1. Panel a) measures \(48^\circ\). 2. Panel b) measures \(132^\circ\). 3. Panel b) is greater by \(132^\circ - 48^\circ = 84^\circ\).

a) \(48^\circ\) b) \(132^\circ\) Panel b) is greater by \(84^\circ\).

- Decide from the picture whether the angle should be acute, right, or obtuse before trusting a scale reading. - Start with the protractor scale whose zero is on ray \(a\). - At one protractor tick, the two printed scales give supplementary readings; choose the one consistent with the opening shown.

1. Align the protractor's zero with ray \(a\). Ray \(b\) meets the correct scale at \(128^\circ\). 2. The other scale at the same tick reads \(52^\circ\), so Jordan likely read the scale that starts from the opposite side. 3. The drawn angle is obtuse, while \(52^\circ\) is acute, so the reported measure is not reasonable.

\(128^\circ\). Jordan likely read the opposite protractor scale; \(52^\circ\) is acute, but the drawn angle is obtuse.