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Two angles of a quadrilateral measure 301° and 10°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?

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Answer:

Explanation:

The sum of the angles of a quadrilateral is 360°. We know that the measures of two angles are 301° and 10°.

Let x be the measure of the smaller of the other two angles, and let y be the measure of the larger of the two angles.

We know that x:y = 2:5, so we can write y = (5/2)x.

Using the fact that the sum of all four angles is 360°, we can write an equation:

301° + 10° + x + y = 360°

Substituting y = (5/2)x, we get:

301° + 10° + x + (5/2)x = 360°

Combining like terms, we get:

311° + (7/2)x = 360°

Subtracting 311° from both sides, we get:

(7/2)x = 49°

Multiplying both sides by 2/7, we get:

x = 14°

So the smaller of the two angles is 14°.

Using y = (5/2)x, we get:

y = (5/2) × 14° = 35°

Therefore, the measures of the two angles are 14° and 35°.

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