Question

question
in the diagram below, \\( \overline { a d } \cong \overline { a e } \\), \\( \overline { b a } \parallel \overline { c e } \\), \\( \overline { c b } \parallel \overline { d a } \\) and \\( m \angle b c d = 65 ^ { \circ } \\). find \\( m \angle e \\).
step
angle
reason
1
\\( m \angle b c d = 65 ^ { \circ } \\)
given
2
\\( m \angle a d e = 65 ^ { \circ } \\)
corresponding angles
try \\( m \angle \square = \square ^ { \circ } \\)
select a reason

Explanation:

Step1: Use the property of isosceles triangle

Since \(\overline{AD}\cong\overline{AE}\), triangle \(ADE\) is isosceles. In an isosceles triangle, the base - angles are equal.

Step2: Calculate the measure of \(\angle E\)

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle ADE\), we know \(\angle ADE = 65^{\circ}\). Let \(\angle E=\angle DAE=x\). Then \(x + x+65^{\circ}=180^{\circ}\), \(2x=180^{\circ}- 65^{\circ}=115^{\circ}\), \(x = 57.5^{\circ}\)

Answer:

\(m\angle E = 57.5^{\circ}\)