Question

Finding angle measures between intersecting lines

Answer 1

x = 13⁰

Explanation:

Since AGC is a right angle, AGD is also a right angle

(Sum of angles of straight line is 180, 180 - 90 =90)

Now, DGF + 77 = 90

or, DGF = 90 - 77

DGF = 13

Now we can say that DGF = x because opposite angles formed by intersecting lines are always equal.

So, x = 13⁰

Answer 2

Explanation:

∠EGB = 77 {Vertically opposite angles}

∠CGB = 90°

∠CGE + ∠EGB = ∠CGB

x + 77 = 90

x = 90 - 77

x = 13