Question

AB = BC = AC = AD, l || m, ∠BAE = x, ∠ADF = 5x. Find the measure of angle x.

Answer 1

1. ΔABC is Equilateral: Since AB = BC = AC, ΔABC is an equilateral triangle.

This means ∠BAC = 60°.

2. Alternate Interior Angles: Lines l || m and AC is a transversal.

Therefore, ∠EAC and ∠ACD are alternate interior angles.

∠EAC = ∠BAE + ∠BAC = x + 60°.

So, ∠ACD = x + 60°.

3. ΔACD is Isosceles: Since AC = AD, ΔACD is an isosceles triangle.

This means ∠ADC = ∠ACD.

So, ∠ADC = x + 60°.

4. Linear Pair: ∠ADF and ∠ADC form a linear pair, meaning their sum is 180°.

∠ADF + ∠ADC = 180°

5x + (x + 60°) = 180°

6x + 60° = 180°

6x = 120°

x = 20°

The measure of angle x is 20°.