Answer:
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°.
