Question

1. If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?

3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1, 2 (90 degrees), 3, 4, 5, 6.
6 degrees
24 degrees
66 degrees
90 degrees

2. Mikel is determining if the two triangles below could be similar based on their side lengths.

Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 8 centimeters. Triangle W X U. Side W X is 18 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters.

Which statements accurately describe the triangles? Check all that apply.
The common ratio between the triangles is 3 because StartFraction 18 Over 6 EndFraction = 3.
The common ratio between the triangles is 2.5 because StartFraction 7.5 Over 3 EndFraction = 2.5.
The triangles could be similar.
The triangles could not be similar.
The ratios of the side lengths are not consistent.
The ratios of the side lengths are consistent.

3. In the diagram, the measure of angle 5 is (10x – 9)°, and the measure of angle 7 is (9x)°. What is the measure of angle 6, to the nearest degree?

A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 6, to the nearest degree?
81°
90°
99°
105°

4. Using side lengths only, could the triangles be similar?

Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.
Yes, StartFraction 0.5 Over 1 EndFraction = StartFraction 0.5 Over 1 EndFraction.
Yes, One-half = StartFraction 0.5 Over 1 EndFraction.
Yes, StartFraction 1.5 Over 1 EndFraction = StartFraction 2 Over 1.5 EndFraction.

Answer 1

1. 24°.
Work: Opposite angles repeat, so angle1 = angle4 = 11x and angle2 = angle5 = 90°. Since angle1 + angle2 + angle3 = 180, 11x + 90 + 4x = 180 → 15x = 90 → x = 6 → angle3 = 4x = 24°.

2. Correct choices:
- The triangles could not be similar.
- The ratios of the side lengths are not consistent.
Reason: Compare side ratios in corresponding order — they are not all equal (e.g., 18/6 = 3, 15/6 = 2.5, 18/8 = 2.25), so no single common scale factor.

3. 99°.
Work: angle5 = 10x − 9 and angle7 = 9x. With parallel lines angle5 = angle1 and angle7 = angle3, and angle1 = angle3, so 10x − 9 = 9x → x = 9. Then angle6 is supplementary to angle5: 180 − (10·9 − 9) = 180 − 81 = 99°.

4. Choose: No, 0.5/1 ≠ 1/1.5 ≠ 1.5/2.
Reason: Sorted side ratios give 1/0.5 = 2, 1.5/1 = 1.5, 2/1.5 ≈ 1.333 — not equal, so the triangles are not similar.