Question

Find the value of x. The diagram is not to scale. Given: ∠SRT ≅ ∠STR, m∠SRT = 28, m∠STU = 4x

Answer 1

Answer:

The value of x is 38°

Step-by-step explanation:

Given: ∠SRT ≅ ∠STR, m∠SRT = 28°, m∠STU = 4x

We are given ∠SRT = ∠STR

But ∠SRT = 28°

Therefore, ∠STR = 28°

Supplementary Angle: Sum of of two angles on straight line is 180°

∠STR + ∠STU = 180°

   28° +  4x     = 180°

                4x  = 180 - 28

                4x  = 152

                  x  = 38°

Hence, The value of x is 38°

               

Answer 2

Given

∠SRT ≅ ∠STR

m∠SRT = 28,  m∠STU = 4x

Find the value of x.

To proof

As given

m∠SRT = 28

Thus

∠STR = 28  

( As given ∠SRT ≅ ∠STR )

∠STU +∠ STR = 180°

( by Linear pair property )

put the value of∠STR in the above equation

we get

∠STU = 180 - 28

∠STU = 152°

∠STU = 4x

thus we get

4x = 152°

x = 38°

Hence proved