Question

Find the measure of the unknown angle, Give Step by step explanation

Answer 1

In Δ ACB :

35 + x + z = 180°   { Angles sum property of Δ }

x + z = 180 - 35

x + z = 145  _____(i)

∠DGE = ∠GCF = 95   { Alternate angles }

Now ,

∠GCF + y = 180    { Linear angles }

95 + y = 180

y = 180 - 95

y = 85

Also ,

y + x = 180    { Linear angles }

85 + x = 180

x = 180 - 85

x = 95

Putting value of x in (i) equation :

x + z = 145

95 + z = 145

z = 145 - 95

x = 50