Question

Please help!!!

Find the indicated measures using the diagram below

Answer 1

x = 60°, y = 78°, z = 29°.

Explanation:

(x). Alternate exterior angles are congruent, so ∠OSP ≅∠HJP, and ∠OSP measures x°. Of the given information, we know ∠HJP = 60°.

• ∠x = 60°.

(y). Vertical angles are congruent, so: ∠OPS ≅∠JPH, and in the diagram ∠OPS measures y°. To find ∠JPH, subtract the other angle measures in this triangle within the quadrilateral. This is represented by: 180 - (60+42) = 78°.

• Since ∠y ≅∠JPH, both angles measure 78°.
• (This can also be found by knowing 102 + y = 180 degrees, which simplifies to y = 78° since they are supplementary angles).

(z). Similar to the first variable's solution, z is the measure of ∠SHP, which is congruent to ∠JOP. Of the given information, we know ∠JOP = 29°. z° is the measure of its alternate, so it is congruent.

• ∠z = 29°