Question

I need help on a khan academy assignment I’m not exactly the brightest bulb...

Answer 1

∠x = 31°

Explanation:

∠x = ∠KAI

∠KAI = ∠BAC through vertical angles.

∠JCG = ∠ACB through vertical angles

∠BAC = ∠x

∠ACB = 59°

∠ABC = 90° because it is a right angle formed by a perpendicular bisector.

Now,

x + 59° + 90° = 180° because the total angle of a triangle is 180°.

x + 149° = 180°

x = 180° - 149°

x = 31°

Answer 2

x= 31

Explanation:

KL⊥ FG

∠ABC = 90°

∠ACB = GCJ {VERTICALLY OPPOSITE ANGLES}

∠ACB = 59°

In ΔABC,

∠ABC + ∠ACB + ∠BAC = 180° {angle sum property of triangle}

90° + 59° + ∠BAC = 180°

149° + ∠BAC = 180°

∠BAC = 180° - 149°

∠BAC = 31°

x = ∠BAC {Vertically opposite angles}

x = 31°