In triangle ABC, AC=BC. The point D is on BC such that AB=AD=DC. Compute the measure of angle C
Let's denote the measure of angle C as x.
Since AC = BC, triangle ABC is an isosceles triangle. Therefore, angle A = angle B.
In triangle ABD, AB = AD, which means that angle ADB is also x degrees.
In triangle ACD, AD = DC, which means that angle DAC is also x degrees.
Now, we can consider triangle ADC. The sum of the angles in a triangle is always 180 degrees.
Therefore, we can write: x + x + x = 180 3x = 180
Dividing both sides by 3, we get: x = 60 So, the measure of angle C is 60 degrees.
