Question

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

N ∈ KO


Answer:
x =?

Answer 1

The value of x in this case is 34°.

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°.