Question

a quadrilateral has two angles that measure 56° and 278°. the other two angles are in a ratio of 5:8. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the two known angles

$56^{\circ}+ 278^{\circ}=334^{\circ}$

Step2: Find the sum of the other two angles

The sum of the interior - angles of a quadrilateral is $360^{\circ}$. So the sum of the other two angles is $360^{\circ}-334^{\circ} = 26^{\circ}$.

Step3: Set up an equation based on the ratio

Let the two angles be $5x$ and $8x$. Then $5x + 8x=26^{\circ}$, which simplifies to $13x = 26^{\circ}$.

Step4: Solve for $x$

$x=\frac{26^{\circ}}{13}=2^{\circ}$

Step5: Find the measures of the two angles

The first angle is $5x = 5\times2^{\circ}=10^{\circ}$, and the second angle is $8x = 8\times2^{\circ}=16^{\circ}$.

Answer:

$10$ and $16$