Answer to Question #100669 in Geometry for Marissa

Question

In ABC, if measure or angle A is six less than seven times x, measure of angle B is five less than three times x, and measure of angle C is five less than four times x, find x and the measure or each angle

Answer 1

Given: triangle with angles A, B and C.

Let x be an unknown variable.

According to task, we get

A = 7x-6, B = 3x-5, C = 4x-5.

According to properties of the triangle, the sum of all interior angle measures is equal to 180 degrees.

Thus, A + B + C = 180;

(7x-6) + (3x-5) + (4x-5) = 180;

14x = 196;

x = 14.

According to this, each angle measures are

A = 7 * 14 - 6 = 92 ;

B = 3 * 14 - 5 = 37 ;

C = 4 * 14 -5 = 51.

Check:

92 + 37 + 51 = 180.