Question

In the given figure, point S is equidistant from the points A and K. If ∠ACS = (3x+33)° and ∠KCS = 45°, then find the value of x.

Answer 1

Let us take Δ ASC and Δ KSC.
AS = KS .......(given)
∠ SKC = ∠ SAC ......(both are 90°)
CS = CS .......(common side)

ΔASC ≅ ΔKSC .......(by RHS congruency rule)

Hence, ∠ KCS = ∠ ACS ......(using CPCT)
3x + 33 = 45
3x = 45 - 33
x = 12/3
= 4