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Question 18 of 22
A home has a triangular backyard. The second angle of the triangle is 4º more than the first angle. The third angle is 16° more than three times the first angle. Find the
angles of the triangular yard.

Answer 1

32°, 36°, 112°

Explanation:

All of the angles are described in terms of the first angle, so we can use a variable to represent that: x. The second angle is (x+4) and the third angle is (3x+16). As always, the sum of angles in a triangle is 180 degrees:

x +(x +4) +(3x +16) = 180

5x +20 = 180 . . . . . collect terms

5x = 160 . . . . . . . subtract 20

x = 32 . . . . . . . divide by 5

x+4 = 36 . . . . find the other two angles

3x+16 = 3(32) +16 = 112

The angles of the triangular yard are 32°, 36°, and 112°.