Given an isosceles triangle ABC, in which AB = BC, angle B = 52 degrees, CD-bisector of angle C.

Given an isosceles triangle ABC, in which AB = BC, angle B = 52 degrees, CD-bisector of angle C. Find the value of the angle CDA by performing the following chain of calculations: angle A =, angle BCA =, angle DCA =, angle CDA =.

Since this isosceles triangle ABC is isosceles, the angles A and C are equal to each other. In addition, the angles of a triangle add up to 180 °. In this way,

angle A = angle C = (180 ° – angle B) / 2 = (180 ° – 52 °) / 2 = 64 °.

The BCA is 64 ° C.

The DCA angle is equal to half of the BCA angle (64 ° / 2 = 32 °) since CD is the bisector of the C angle by condition.

In the DCA triangle, the angle DCA = 32 ° and the angle A = 64 ° are known. So,

CDA angle = 180 ° – DCA angle – A = 180 ° – 32 ° – 64 ° = 84 °.