A quadrilateral has two angles that measure 248° and 56°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
The sum of interior angles in a quadrilateral is 360°. Let's call the two unknown angles "2x" and "5x".
We know that:
248° + 56° + 2x + 5x = 360°
Simplifying:
304° + 7x = 360°
Subtracting 304° from both sides:
7x = 56°
Dividing both sides by 7:
x = 8°
So the two unknown angles are:
2x = 16°
5x = 40°
To find the measures of the other two angles, let's assign variables to them.
Let the measures of the two angles be 2x and 5x, where x is a constant.
According to the problem, the sum of all angles in a quadrilateral is 360°. So, we can create an equation:
248° + 56° + 2x + 5x = 360°
Combining like terms, we have:
304° + 7x = 360°
Next, we can subtract 304° from both sides of the equation:
7x = 360° - 304°
Simplifying further:
7x = 56°
Now, we can solve for x by dividing both sides of the equation by 7:
x = 56° / 7
x = 8°
To find the measures of the other two angles, substitute the value of x back into the expressions:
2x = 2 * 8° = 16°
5x = 5 * 8° = 40°
Therefore, the measures of the other two angles are 16° and 40°.