D=b^2-4ac solve for a
1 answer:
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Answer:
5. ∠TSR ≅ ∠TRS = 72°
6. ∠ORS ≅ ∠OSR = 18°
7. ∠ROS = 144°
Step-by-step explanation:
Segments OT and SR can be drawn to divide the figure into similar right triangles. In these triangles, all of the smaller acute angles are congruent, and all of the larger acute angles are congruent. The smaller and larger acute angles are complementary, as they are in any right triangle.
Segment OT bisects angle T, so the smaller acute angle in each right triangle is 36°/2 = 18°.
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<h3>5.</h3>∠TSR ≅ ∠TRS = 90° -18° = 72°
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<h3>6.</h3>∠ORS ≅ ∠OSR = 18°
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<h3>7.</h3>∠ROS = 2×∠TOS = 2×72° = 144°
Note that this is supplementary to ∠T: ∠O = 180° -36° = 144°.
