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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....​

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 mea class=

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

Step-by-step 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°.

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