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°.