Question

in the diagram below, $overline{bc}congoverline{ec}$ and $mangle ecd = 124^{circ}$. find $mangle abe$. you may assume lines that appear straight are straight, but the figure is not otherwise drawn to - scale. answer attempt 1 out of 2 $mangle abe=square$

Explanation:

Step1: Find m∠BCE

Since ∠ECD and ∠BCE are a linear - pair (they form a straight line), and m∠ECD = 134°.
We know that m∠ECD+m∠BCE = 180°.
So, m∠BCE=180° - 134° = 46°.

Step2: Use the property of isosceles triangle

Given BC ≅ EC, triangle BCE is an isosceles triangle. In an isosceles triangle △BCE, ∠EBC=∠BEC.
Let m∠EBC = m∠BEC = x.
Using the angle - sum property of a triangle (the sum of the interior angles of a triangle is 180°) in △BCE, we have x + x+46° = 180°.
Combining like terms gives 2x=180° - 46° = 134°.
Dividing both sides by 2, we get x = 67°.

Step3: Find m∠ABE

∠ABE and ∠EBC are a linear - pair.
So, m∠ABE = 180°-m∠EBC.
Since m∠EBC = 67°, then m∠ABE = 180° - 67° = 113°.

Answer:

113°