IXL | Triangle Angle-Sum Theorem

The diagram shows a convex polygon.

54°

What is the value of

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question

The diagram shows a convex polygon.

76°

What is the value of

key idea

The sum of the interior angle measures of a triangle is 180°.

solution

First, find the sum of the interior angle measures of the convex polygon. The polygon is a triangle, so the sum of the interior angle measures is 180°.

Next, look at the interior angle measures in the triangle.

Set the sum of the interior angle measures of the triangle equal to 180°. Solve for

76°

180°

76°

Combine like terms

180°

Combine like terms

Subtract 76° from both sides

104°

Subtract 76° from both sides

Divide both sides by 8

13°

Divide both sides by 8

So,

13°

Looking for more? Try these:

Lesson: Interior angles of triangles

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Z.8Find missing angles in triangles

T.14Solve equations involving like terms

Lesson: Interior angles of triangles

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