Angle Relationships

Determine the value of angle WXY.

• 115°

• 65°

• 47°

• 68°

Line L is parallel to line M. Both lines are intersected by line Q. What is the measure of ∠x?

• 108°

• 62°

• 72°

• 252°

Triangle CAT and Triangle DOG are similar. What is the measure of ∠T?

• 55°

• 57°

• 68°

• 123°

In the diagram, Line E is parallel to line F, and both lines are intersected by line V. Based on the diagram, which statement is true?

• The measure of ∠N is 137° because the labeled angles are supplementary.

• The measure of ∠N is 47° because the sum of the labeled angles equals 90°.

• The measure of ∠N is 43° because the labeled angles are congruent.

• The measure of ∠N is 57° because the sum of the labeled angles equals 100°.

A triangle is shown. One side of the triangle lies along a ray. Based on the diagram, which statement best describes the measure of ∠P?

• ∠P = 74° because 85 + 21 = 106 and 180 - 106 = 74.

• ∠P = 286° because 85 + 21 = 106 and 180 + 106 = 286.

• ∠P = 95° because 180 - 85 = 95.

• ∠P = 106° because 180 - (85 + 21) = 74 and 180 - 74 = 106.

In the diagram, triangle ABC and triangle XYZ are both right triangles. ∠A is congruent to ∠X. Which statement about the triangles must be true?

• The measure of ∠B is less than the measure of ∠Y because triangle ABC is smaller than triangle XYZ.

• The measure of ∠B is the same as the measure of ∠Y because triangle ABC and triangle XYZ are similar.

• The measure of ∠B is the same as the measure of ∠Y because triangle ABC and triangle XYZ are congruent.

• The measure of ∠B is greater than the measure of ∠Y because triangle ABC and triangle XYZ are similar.

In each diagram, line r and line s are parallel. Both lines are intersected by line t. Based on the diagram, what is the value of x?

• x = 58° because the angles shown in each diagram are supplementary.

• x = 32° because the angles shown in each diagram are complementary.

• x = 122° because the angles shown in each diagram are congruent.

• The value of x cannot be determined based on the diagram.

A triangle is shown with one side extended to form a ray. What is the measure of ∠m?

• 118°

• 135°

• 45°

• 62°

In each diagram, line h and line j are parallel. Both lines are intersected by line m. Based on the diagrams, what is the value of x?

• x = 119° because the angles shown in each diagram are supplementary.

• x = 61° because the angles shown are congruent.

• x = 29° because the angles shown are complementary.

• x = 151° because the difference between the angles shown is 90°.

Triangle QRS is similar to triangle TUV. Angle R is congruent to angle U. Angle S is congruent to angle V. Based on the diagram, what is the measure of angle Q?

• Angle Q measures 17° because angle R measures 63 and 80 - 63 = 17.

• Angle Q measures 50° because 180 - 80 = 100 and 100 ÷ 2 = 50.

• Angle Q measures 37° because angle R measures 63 and 180 - (63 + 80) = 37.

• There is not enough information to determine the measure of angle Q.