Two angles of a quadrilateral measure 272° and 34°. The other two angles are in a ratio of 2:7. What are the measures of those two angles?
Question
Two angles of a quadrilateral measure 272° and 34°.
The other two angles are in a ratio of 2:7. What are the measures of those two angles?
Solution
Sure, here are the steps to solve the problem:
Step 1: Add the two given angles. 272° + 34° = 306°
Step 2: Subtract the sum from 360° (since the sum of all angles in a quadrilateral is 360°). 360° - 306° = 54°
Step 3: Now, the remaining two angles are in the ratio 2:7. So, divide 54° by the sum of the ratio (2+7=9). 54° ÷ 9 = 6°
Step 4: Multiply this result by each part of the ratio to find the measures of the two angles. 2 * 6° = 12° 7 * 6° = 42°
So, the measures of the two remaining angles are 12° and 42°.
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