Question

I am trying to understand how to solve for X, then solve the equation

Answer 1

Answer:

x = 16

m<Y = 34°

Step-by-step explanation:

∆XYZ is an isosceles ∆. An isosceles ∆ has two equal sides, as well as the bases of the isosceles triangle are congruent. In this case, therefore:

<X = <Z

(6x - 23)° = (4x + 9)

Solve for x

6x - 23 = 4x + 9

Collect like terms

6x - 4x = 23 + 9

2x = 32

Divide both sides by 2

x = 16

m<Y = 180° - (m<X + m<Z) (sum of ∆)

m<Y = 180 - ((6x - 23) + (4x + 9))

Plug in the value of x

m<Y = 180 - ((6(16) - 23) + (4(16) + 9))

m<Y = 180 - (73 + 73)

m<Y = 34°