Topic 6 Triangle Relationships Review

Name a pair of Vertical Angles.

• ∠AOB and ∠COD

• ∠AOD and ∠BOC

• ∠BOE and ∠AOD

• ∠AOC and ∠BOD

Answer explanation

Vertical angles are formed by two intersecting lines. ∠AOB and ∠COD are opposite angles created by the intersection, making them vertical angles. The other options do not represent pairs of vertical angles.

What is the measure of ∠LMQ?

• 25°

• 40°

• 115°

• 180°

Answer explanation

To find the measure of ∠LMQ, we can use the properties of angles in a triangle or supplementary angles. Given the options, 115° is the only angle that fits typical angle measures in geometric contexts.

Find the value of x in the triangle where angle A = 62°, angle B = 57°, and angle D = (3x - 28)°.

• x = 41

• x = 49

• x = 53

• x = 45

Answer explanation

In triangle ABC, the sum of angles is 180°. Thus, 62° + 57° + (3x - 28)° = 180°. Simplifying gives 3x = 89, so x = 49. Therefore, the correct answer is x = 49.

Find the width of the foundation.

• 60 ft

• 70 ft

• 75 ft

• 65 ft

What is the sum of the measures of the interior angles of a regular octagon?

• 180 (8-2) degrees

• 180 * 8 degrees

• 180 (8+2) degrees

• 180(8-2) ÷ 8 degrees

Answer explanation

The sum of the interior angles of a polygon is given by the formula 180(n-2), where n is the number of sides. For a regular octagon (8 sides), it is 180(8-2) degrees, which simplifies to 1080 degrees.

Find the exact distance from point A to point B on the coordinate plane.

• √5 units

• √40 units

• 40 units

• √50 units

Name a pair of Supplementary Angles.

• ∠AOB and ∠BOC

• ∠AOD and ∠DOC

• ∠DOE and ∠AOD

• ∠AOC and ∠BOD

Answer explanation

∠AOB and ∠BOC are supplementary angles because their measures add up to 180 degrees. This makes them a valid pair of supplementary angles, while the other options do not necessarily meet this criterion.

What is the measure of angle x in the triangle shown?

• 44°

• 45°

• 46°

• 47°

Answer explanation

In a triangle, the sum of the angles is 180°. If the other two angles are 68° and 68°, then angle x = 180° - 68° - 68° = 44°. Thus, the measure of angle x is 44°.

Two sides of a triangle measure 12 and 22 cm. What are possible measures for the third side? (Select all that apply.)

• 7 cm

• 10 cm

• 14 cm

• 27 cm

• 36 cm

Answer explanation

The third side of a triangle must be less than the sum and greater than the difference of the other two sides. Thus, it must be less than 34 cm (12 + 22) and greater than 10 cm (22 - 12). Therefore, 14 cm and 27 cm are valid.

What is the measure of one interior angle of a regular octagon?

• 135 degrees

• 120 degrees

• 140 degrees

• 150 degrees

Answer explanation

To find the measure of one interior angle of a regular octagon, use the formula: (n-2) * 180° / n, where n is the number of sides. For an octagon (n=8), it becomes (8-2) * 180° / 8 = 135°. Thus, the correct answer is 135 degrees.