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please help!!!

Find the indicated measures using the diagram below

Please Help Find The Indicated Measures Using The Diagram Below class=

Sagot :

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Answer:

x = 60°, y = 78°, z = 29°.

Step-by-step 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°

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