Question

What is the value of x? Enter your answer in the box. x =

Answer 1

Answer:

x=32

Step-by-step explanation:

We are given that a triangle XYZ in which

XY=YZ=ZY

$\angle Z=2x-4, \angle Y=5y$

We have to find the value of x.

We know that when all sides of triangle are equal then, the triangle is equilateral triangle and  each angle of equilateral triangle is equal to 60 degrees.

$\angle X=\angle Y=\angle Z=60^{\circ}$

$2x-4=60^{\circ}$

Using substitution property of equality

$2x=60+4=64$

$x=\frac{64}{2}=32$

Hence, the value of x=32

Answer 2

Angle sum of a triangle = 180°

Therefore:

Equation No. 1 -
2 ( 2x - 4 ) + 5y = 180°
2 ( 2x - 4 ) + 5 [ ( 2x - 4 ) / 5 ] = 180
4x - 8 + [ 5 ( 2x - 4 ) / 5 ] = 180
4x - 8 + 2x - 4 = 180
4x + 2x = 180 + 8 + 4
6x = 192
x = 192 / 6
x = 32°

Equation No. 2 -
5y = 2x - 4
y = ( 2x - 4 ) / 5

ANSWER:
x = 32°