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I need help with 37 38 39

I need help with 37 38 39-example-1
User Kakia
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We presume you want the values of the variables shown.

37) In a parallelogram, opposite angles are congruent. That means ...

104° = 2x

... x = 52°

76° = 2w

... w = 38°

The sum of angles of a triangle is 180°, so ...

... w + x + y = 180°

... y = 180° - 38° - 52°

... y = 90°

38) The sum of angles around a circle is 360°.

... c + 2c + 3c + 126° = 360°

... 6c = 360° - 126° = 234°

... c = 234*/6 = 39°

39) PQ ║ BC, so ∠APQ = ∠ABC

∆AQB is isosceles, so ∠A = ∠ABQ

The sum of angles of triangle ABC is 180°, so

∠A + (∠A +28°) +52° = 180°

2∠A = 100° . . . . . . collect terms, subtract 80°

∠A = 50° . . . . . . . . divide by 2

Now, you know all the parts that make up ∠ABC.

∠ABC = ∠A + 28° = 50° +28° = 78°

∠APQ = 78°

User Prashant Puri
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