Question

In the diagram below, overline BE perp overline ED , overline AC cong overline BC . and m angle A=70^ . Find m angle D .

Answer 1

As segment AC is congruent to segment BC, then we can conclude that ΔACB is an isosceles triangle.

In an isosceles triangle, the base angles (in this case, ∠A and ∠B) have the same measure. Thus:

`m\angle A=m\angle B`
`m\angle B=70`

Based on the latter, we can get m∠C knowing that the addition of the interior angles of a triangle add up to 180°:

`m\angle A+m\angle B+m\angle C=180`
`m\angle C=180-m\angle A-m\angle B`
`m\angle C=180-70-70`
`m\angle C=40`

As ∠C has two opposite angles, then the measure of each is the same. Finally, following the same logic, to get m∠D we have to subtract ∠C and ∠E from 180° as follows:

`m\angle E+m\angle D+m\angle C=180`
`m\angle D=180-m\angle E-m\angle C`
`m\angle D=180-90-40`
`m\angle D=50`

Answer: 50°