Question

two angles of a quadrilateral measure 258° and 56°. the other two angles are in a ratio of 10:13. what are the measures of those two angles?

Explanation:

Step1: Find total of known angles

$258^\circ + 56^\circ = 314^\circ$

Step2: Find sum of unknown angles

The sum of interior angles of a quadrilateral is $360^\circ$.
$360^\circ - 314^\circ = 46^\circ$

Step3: Calculate ratio total parts

$10 + 13 = 23$

Step4: Find value of one part

$\frac{46^\circ}{23} = 2^\circ$

Step5: Compute first unknown angle

$10 \times 2^\circ = 20^\circ$

Step6: Compute second unknown angle

$13 \times 2^\circ = 26^\circ$

Answer:

$20^\circ$ and $26^\circ$