Question

The measure of each of the

congruent angles of an isosceles
triangle is 9 less than 4 times the
vertex angle. Find the measures of all
the angles in the triangle.

Answer 1

22°, 79° and 79°

Explanation:

Let x be the vertex angle and y each of the congruent angles.

The sum of all angles =180°

So x + y + y = 180

x + 2y = 180 ·········· Equation (1)

Given "The measure of each of the congruent angles of an isosceles triangle is 9 less than 4 times the vertex angle", the equation is

y = 4x - 9

Substitute for y in terms of x in equation 1

⇒ x + 2(4x - 9) = 180

⇒ x + 8x - 18 = 180

⇒ 9x - 18 = 180

⇒ 9x = 180 + 18

⇒ 9x = 198

⇒ x = 198/9 = 22

So vertex angle is 22°

Substituting for x in Equation 1:
22 + 2y = 180
2y = 180 - 22
2y = 158
y = 158/2
y = 79°

So each congruent angle is 79°