Question

What is the measure of ZCED?

60
С
E
60"
m, because AABC - AEDC
N13
because AABC ADCE
m+ 60 degrees, because AABC - ADCE
O 120 degrees
m, because AABC ADCE

Answer 1

The correct option is A.

A) m, because ΔABC ~ ΔEDC

Explanation:

Consider the both triangles.

<B = 60°

<D = 60°

<B and <D are congruent

<ACB = 90°

<DCE = 90°

<ACB and < DCE are also congruent.

As sum of the angles of triangle is 180°

<A = 180° - <ACB - <B

<A = 180° - 90° - 60

<A = 30° = m

<E = 180° - <DCE - <D

<E = 180° - 90° - 60°

<E = 30°

As m = 30°

<E = <CED = m

As segment AD cuts segment BE, which results in formation of two triangle, and as all angles of both triangles are equal, both triangles are similar.