IXL | Find missing angles in triangles using ratios

A triangle has an angle that measures 95°. The other two angles are in a ratio of 3:14. What are the measures of those two angles?

° and °

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A triangle has an angle that measures 110°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?

° and °

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

Since the angles are in a ratio of 3:4, they have measures of 3n and 4n. Set the sum of the angle measures equal to 180° and solve.

110° + 3n + 4n

180°

Combine like terms

110° + 7n

180°

Combine like terms

Subtract 110° from both sides

180° − 110°

Subtract 110° from both sides

Simplify

70°

Simplify

Divide both sides by 7

10°

Divide both sides by 7

Now plug in n = 10° to find the measures of the angles.

3n and 4n

3 × 10° and 4 × 10°

30° and 40°

So, the measures of the two angles are 30° and 40°.

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