IXL | Find missing angles in triangles using ratios

One angle of a triangle measures 85°. The other two angles are in a ratio of 9:10. What are the measures of those two angles?

° and °

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question

One angle of a triangle measures 85°. The other two angles are in a ratio of 2:17. What are the measures of those two angles?

° and °

key idea

The measures of the angles of a triangle add up to 180°.

solution

Since the angles are in a ratio of 2:17, they have measures of 2n and 17n. Set the sum of the angle measures equal to 180° and solve.

85° + 2n + 17n

180°

Combine like terms

85° + 19n

180°

Combine like terms

Subtract 85° from both sides

19n

180° − 85°

Subtract 85° from both sides

Simplify

19n

95°

Simplify

Divide both sides by 19

5°

Divide both sides by 19

Now plug in n = 5° to find the measures of the angles.

2n and 17n

2 × 5° and 17 × 5°

10° and 85°

So, the measures of the two angles are 10° and 85°.

Looking for more? Try these:

Lesson: Interior angles of triangles

Lesson: Ratios

Lesson: Solving equations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.8Find missing angles in triangles

T.14Solve equations involving like terms

Lesson: Interior angles of triangles

Lesson: Ratios

Lesson: Solving equations

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