Question

From basic geometry, we know that the angles in a triangle sum to 1800. We also know that when two sides of a triangle are equal, the angles opposite to them are equal. Use these facts to solve the following problem. Triangle ABC in the figure below is an isosceles triangle (the two marked sides are equal): Also, the ratio of the measures of angle A to angle B is 8:5. What is the measure of angle C?

Answer 1

50 degree : By using characteristics of a triangle.

Answer 2

Answer: 50°

Step-by-step explanation:

Here, ABC is an isosceles triangle,

⇒ AB = BC

⇒ ∠B = ∠C

The ratio of the measures of angle A to angle B is 8:5,

Let ∠A = 8x and ∠B = 5x

Where x is any number,

⇒ ∠C = 5x

By the property of a triangle,

∠A + ∠B + ∠C = 180°

⇒ 8x + 5x + 5x = 180°

⇒ 18 x = 180°

⇒ x = 10°

Thus, ∠C = 5x =  50°