Question

What is the measure of angle CED? There are two triangles labeled ABC and DCE with a common vertex C. In triangle ABC, angle BAC is labeled as m, and angle ABC is labeled as 60 degrees. In triangle DCE, angle CDE is labeled as 60 degrees. m, because Triangle ABC is similar to triangle EDC m over 2, because Triangle ABC is congruent to triangle DCE m + 60 degrees, because Triangle ABC is similar to triangle DCE 120 degrees − m, because Triangle ABC is congruent to triangle DCE

Answer 1

The measure of angle CED is m and option 1 is correct.

Explanation:

In triangle ABC and EDC,

`\angle ABC=\angle EDC=60^(\circ)` (Given)

`\angle ACB=\angle ECD` (C is common vertex)

By AA property of similarity,

`\triangle ABC\sim \triangle EDC`

If two triangles are similar, then their corresponding angles are same and the corresponding sides are proportional.

Since triangle ABC is similar to triangle EDC, therefore

`\angle CAB=\angle CED`

`m=\angle CED`

Therefore the measure of angle CED is m. Option 1 is correct.