Question

In △ABC , m∠A=72° , m∠B=(8y−16)° , and m∠C=(9x)° . Isosceles triangle ABC. AB is the base, lateral sides AC and CB are marked congruent. What are x and y?

Answer 1

ΔABC = isosceles => ∡B = ∡C

∡B = ∡C = (180°-72°) : 2 = 108° : 2 = 54°

∡B = 54° = 8Y - 16

54 + 16 = 8Y

70 = 8Y

Y = 8.75°

∡C = 54° = 9X

X = 54 : 9

X = 6°

Answer 2

The values of x and y are as follows:

$x = 4\\\\y =11$

Given that:

△ABC  is isosceles

AC and BC are congruent.

∠A=72°

∠B=(8y−16)°

∠C=(9x)°

AB is the base.

Calculations:

Since ABC triangle is isosceles and AC and BC are congruent, thus we have:

$\angle A = \angle B\\72 = 8y - 16\\8y = 88\\y = 11$

Since all angles of a triangle sums up to 180 degrees, thus we have:

$\angle A + \angle B + \angle C = 180^\circ\\72 + 72 + 9x = 180\\9x = 180 - 144\\9x = 36\\x = 4$

Thus, the values of x and y are as follows:

$x = 4\\\\y =11$

Learn more about isosceles triangles here:

https://brainly.com/question/7915845