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Home > GC > Chapter 11 > Lesson 11.1.3 > Problem 11-45

11-45.

Sum of interior angles = 180(n − 2) = 180(5 − 2) = 540°

Therefore, 90 + 4x + (8x − 10) + 90 + (6x + 4) = 540

x² + (x + 17)² = 25²

x² + (x² + 34x + 289) = 625

You can ultimately solve this problem by factoring.

x = 7

Note that because the figure is an isosceles triangle, two angles are equal to x + 4° and the remaining angle is equalto 46°, since it is supplementary to the angle of 134°.

x = 63°

(3x + 15) + (x + 9) = 180°