If triangle ABC is isosceles and triangle DBE is equilateral what is the measure of angle C

43°

Step-by-step explanation:

For triangle ABC:

A = C so all we need to do is to calculate the value of B

The measure of angle ABD is given as 17° so the measure of angle EBC must be 17° as well

Since DBE is an equilateral triangle angle is DBE = 60°

17 + 17 + 60 = 94 this is the measure of angle B

The sum of interior angles in a triangle is equal to 180

A + B + C = 180

A + C + 94 = 180

A + C = 86 since A = C we divide 86 by 2

C = 43°