The sum of the angles in a quadrilateral is 360°.
Let's call the two unknown angles x and y.
We know that x:y is in a ratio of 3:7, so we can write x=3a and y=7a for some value of a.
Then we can set up an equation:
278° + 2° + x + y = 360°
Substituting in our expressions for x and y:
278° + 2° + 3a + 7a = 360°
Combining like terms:
280° + 10a = 360°
Subtracting 280° from both sides:
10a = 80°
Dividing by 10:
a = 8°
So now we know that x = 3a = 24° and y = 7a = 56°.
Therefore, the measures of the two unknown angles are 24° and 56°.
A quadrilateral has two angles that measure 278° and 2°. The other two angles are in a ratio of 3:7. What are the measures of those two angles?
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