Question

Find the values of x and y

Answer 1

x = 90 , y = 37

Explanation:

given AB and AC are congruent , then Δ ABC is isosceles with base angles also congruent, then

∠ ABD = ∠ ACD = 53°

given ∠ BAD = ∠ CAD = y°

The sum of the 3 angles in Δ ABC = 180° , then

∠ BAC = 180° - (53 + 53)° = 180° - 106° = 74° , then

y = 74 ÷ 2 = 37

and in Δ ABD

x + y + 53 = 180

x + 37 + 53 = 180

x + 90 = 180 ( subtract 90 from both sides )

x = 90