ABC is an isosceles triangle. AC is the base. angle A = C = 70 °. D – the point of intersection of the bisectors

ABC is an isosceles triangle. AC is the base. angle A = C = 70 °. D – the point of intersection of the bisectors of the angles at the base. Find the degree measure of the ADC angle.

1. The bisector АD divides the angle ∠А, from which it is drawn into two equal angles

∠CAD = BAD = ∠A: 2 = 70 °: 2 = 35 °.

2. The bisector CD also divides the angle from which it is drawn into two equal angles

∠АСD = ВСD = ∠С: 2 = 70 °: 2 = 35 °.

3. We calculate the value of ∠ADC, taking into account that the total value of the angles of the triangle ADC is 180 °:

∠АСD + ∠САD + ∠ADС = 180 °.

∠АDС = 180 ° – (∠АСD + ∠САD) = 180 ° – (35 ° + 35 °) = 180 ° – 70 ° = 110 °.

Answer: the sought ∠ADC is 110 °.