Question

An artist is designing a triangular pane of glass for a stained glass window, as shown in the diagram. Given that measure ABC is an exterior angle, what is the measure of each interior angle of the triangle? Explain your reasoning. I put the picture of the triangle by the way....​

Answer 1

The measure of the interior angles of the triangle are 60, 80 and 40

From the triangle given; The measure of ∠CBD is :

• ∠CBD = 180 - 120 = 60° (sum of angles on a straight line)

Using the value of CBD obtained ;

∠C + ∠B + ∠D = 180° (sum of angles in a triangle)

2x + x + 60 = 180

3x + 60 = 180

3x = 180 - 60

3x = 120

x = 40

∠C = 2x

• C = 2(40) = 80°

∠D = x

• D = 40

The measure of the interior angles are 60, 80, 40

Answer 2

The value of each interior angle of the triangle is 40°,60° and 80°.

Explanation:

Given,

In ΔBCD, ∠D= x° and ∠C = 2x° and ∠ABC = 120°

To find the value of each interior angle.

We know that,

• The value of exterior angle is equal to the sum of opposite interior angles.

• The sum of all the angles of a triangle is 180°.

Now,

∠BCD+∠BDC = ∠ABC

2x+x = 120°

or, 3x = 120°

or, x = 40°

So, ∠BDC = 40° , ∠BCD = 2×40° = 80°

So, ∠ CBD = 180°-(80°+40°) = 60°

Hence,

The value of each interior angle of the triangle is 40°,60° and 80°.