We know that the sum of all four angles in a quadrilateral is 360 degrees. We can use this to find the measure of the other two angles:
Let x be the measure of the smaller of the two remaining angles.
Then the larger angle has a measure of (7/12)x, since the two angles are in a ratio of 7:12.
We can now write an equation based on the sum of all four angles:
316° + 6° + x + (7/12)x = 360°
Simplifying the equation:
322° + (19/12)x = 360°
(19/12)x = 38°
x = 24°
So the smaller angle has a measure of 24 degrees, and the larger angle has a measure of (7/12)x24 = 42 degrees.
Therefore, the two remaining angles are 24° and 42°.
Two angles of a quadrilateral measure 316° and 6°. The other two angles are in a ratio of 7:12. What are the measures of those two angles?
1 answer