Find the angle of x in the shapes in the image below.  A rectangle, obtuse triangle, and scalene triangle.

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Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

1. The angles EAB and BEA are complementary, their sum is 90° (from the right triangle ABE). Therefore BEA=90°-36°=54°. Next, angles BEA, AED and DEC form a straight angle CEB. So 54°+x+62°=180°, x=180°-54°-62°=64°.

 

2. The angle XZY is the exterior angle for the triangle XZW, therefore XZY=x+32°. Because the triangle XYZ is equilateral, all its angles are the same x+32°. Now consider the triangle XYW and sum its angles:

X+Y+W = (x+32°+x) + (x+32°) + 32° = 3(x + 32°) = 180° = 3*60°,

so x=60°-32°=28°.

 

3. The angle PRQ is the same as the angle PQR, because PQ=PR. And also it is the exterior angle for the triangle PRS. Thus 71°=x+25° and x=71°-25°=46°.