IXL | Find missing angles in triangles using ratios

One angle of a triangle measures 40°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?

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question

A triangle has an angle that measures 70°. The other two angles are in a ratio of 9:13. 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 9:13, they have measures of 9n and 13n. Set the sum of the angle measures equal to 180° and solve.

70° + 9n + 13n

180°

Combine like terms

70° + 22n

180°

Combine like terms

Subtract 70° from both sides

22n

180° − 70°

Subtract 70° from both sides

Simplify

22n

110°

Simplify

Divide both sides by 22

5°

Divide both sides by 22

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

9n and 13n

9 × 5° and 13 × 5°

45° and 65°

So, the measures of the two angles are 45° and 65°.

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:

Q.7Find missing angles in triangles

M.11Solve equations involving like terms

Lesson: Interior angles of triangles

Lesson: Ratios

Lesson: Solving equations

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