Question

Triangle RST is congruent to triangle XYZ. If the measure of angle Ris 32

and the measure of angle S is 45, what is the measure of angle Z?

Answer 1

The measure of angle Z in triangle XYZ, congruent to triangle RST, is 103° because corresponding angles in congruent triangles are equal and the sum of angles in a triangle is 180°.

Step-by-step explanation:

If triangle RST is congruent to triangle XYZ, it means that corresponding angles and sides are equal in measure. Since angle R is 32° and angle S is 45°, we know these two angles add up to 77°. By the triangle sum theorem, the sum of the angles in a triangle is always 180°. Thus, the measure of angle T, the third angle in triangle RST, is 180° - 32° - 45° = 103°.

Corresponding angles in congruent triangles are equal, so angle Z in triangle XYZ will have the same measure as angle T in triangle RST. Therefore, the measure of angle Z is 103°.