Find the value of x in each case. give reasons to justify your solutions!

n ∈ ko


x =?

The value of x in this case is  34°.

Step-by-step explanation:

Here, Lines TR and UP is intersecting lines at the point S.

⇒∠ TSU = ∠ PSR     (VERTICALLY OPPOSITE ANGLES)

⇒ 4x = ∠ PSQ + ∠ QSR  

       = ∠ PSQ  +  3x

⇒ ∠ PSQ = 4x - 3x = x

⇒ ∠ PSQ   = x

Now, by The INTERIOR EXTERIOR ANGLES THEOREM In  a TRIANGLE:

Sum of Two Interior angle of a triangle is equal to opposite exterior angle.

So, here in Δ PSR

∠ PSQ + ∠ SPQ = ∠ SQR

or, x + x = 68°

or, 2 x  = 68°

⇒ x = 68/2  = 34°

Hence, the value of x in this case is  34°.