Question

In the daigram AB ia parallel to CD, and AE is parallel to BC. AB=AC, angle ACD=68° and CDE=110° Find the size of the angle p ,q and r​

Answer 1

p = 68° , q = 44° , r = 114°

Explanation:

∠ ACD = ∠ BAC = p ( alternate angles ) so

p = 68°

Since AB = AC then Δ ABC is isosceles with base angles congruent, that is

∠ BCA = ∠ CAB = 68°

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

68° + 68° + q = 180°

136° + q = 180° ( subtract 136° from both sides )

q = 44°

∠ EAC = ∠ ACB ( alternate angles ) so

∠ EAC = 68°

The sum of the 4 angles in quadrilateral ACDE = 360°

r + 68° + 68° + 110° = 360°

r + 246° = 360° ( subtract 246° from both sides )

r = 114°