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?

1 answer

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°.