Question

If m C=66, find the values of x and y.

A) x = 24, y = 66

B) x = 90, y = 66

C) x = 90, y = 24

D) x = 66, y = 24

Answer 1

Since triangle ABC is a isosceles triangle
∠ABD = 66°
(Base angle of isosceles triangle)

∠BAC = 180° - (66° × 2) = 48°
y = 48° ÷ 2 = 24°
z = 90°

Answer is C.

Answer 2

C) x=90°, y=24°

Explanation:

The two sections into which A is split, are the same size as indicated. Sides AB and AC are the same length. Because of those reasons, it can be concluded that B and C are the same size.

The corners of a triangle adds up to 180°. For ΔABC:

`A+B+C=180\\A+2(66)=180\\A=48`

y° is half of A:

∴y° = 24°

Now add up the corners of triangle ABD:

`y+x+B=180\\24+x+66=180\\x=90`

∴x° = 90°