Question

Can someone help me please?

Answer 1

∠BAD ≅ ∠EDA because they are Alternate Interior Angles

m∠BAD = m∠EDA = 72°

∠B ≅ ∠E therefore m∠B = m∠E = 65°.

AB = AC. Therefore ΔABC is an isosceles triangle. Hence m∠B = m∠C = 65°.

We know: the sum of the measures of the angles in a triangle equals 180°.

Therefore we have the equation:

m∠BAC + m∠B + m∠C = 180°

m∠BAC + 65° + 65° = 180°

m∠BAC + 130° = 180°       subtract 130° from both sides

m∠BAC = 50°

m∠BAD = m∠BAC + x°

72° = 50° + x°    subtract 50° from both sides

22° = x°

x° = 22°