IXL - Interior angles of quadrilaterals (Geometry practice)

Two angles of a quadrilateral measure 100° and 190°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?

° and °

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Two angles of a quadrilateral measure 120° and 20°. The other two angles are in a ratio of 9:13. What are the measures of those two angles?

° and °

The measures of the angles of a quadrilateral add up to 360°.

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 360° and solve.

120° + 20° + 9n + 13n

360°

Combine like terms

140° + 22n

360°

Combine like terms

Subtract 140° from both sides

22n

360° − 140°

Subtract 140° from both sides

Simplify

22n

220°

Simplify

Divide both sides by 22

10°

Divide both sides by 22

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

9n and 13n

9 × 10° and 13 × 10°

90° and 130°

So, the measures of the two angles are 90° and 130°.

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