Question

a quadrilateral has two angles that measure 106° and 46°. the other two angles are in a ratio of 7:9. what are the measures of those two angles?

Explanation:

Step1: Find total of known angles

$106^\circ + 46^\circ = 152^\circ$

Step2: Find sum of unknown angles

The sum of interior angles of a quadrilateral is $360^\circ$.
$360^\circ - 152^\circ = 208^\circ$

Step3: Calculate ratio total parts

$7 + 9 = 16$

Step4: Find value of one part

$\frac{208^\circ}{16} = 13^\circ$

Step5: Compute first unknown angle

$7 \times 13^\circ = 91^\circ$

Step6: Compute second unknown angle

$9 \times 13^\circ = 117^\circ$

Answer:

$91^\circ$ and $117^\circ$