Question

Given the figure to the right and the fact

that m ZABD = 133', find the measure-
ments of the angles below.

Answer 1

∠ABC = 94°

∠BCD = 25°

∠ACB = 43°

Explanation:

∠ABD = 133°

Since △ADC is an isosceles triangle where AD = CD, it means that ∠CBD = 133°

We know sum of angles at a point is 360°.

Thus; ∠ABC = 360 - (133 + 133)

∠ABC = 94°

Now, in △BCD, ∠B = 133° and ∠D = 22°

Sum of angles in a triangle = 180°

Thus; ∠BCD = 180 - (133 + 22)

∠BCD = 25°

Since the △ABC is also an isosceles triangle , it means that;

In △ABC, ∠A = ∠C

Thus; ∠ACB = (180 - 94)/2

∠ACB = 86/2

∠ACB = 43°