Question

two angles of a quadrilateral measure $163^\circ$ and $109^\circ$. the other two angles are in a ratio of 3:5. what are the measures of those two angles? $square^\circ$ and $square^\circ$

Explanation:

Step1: Calculate sum of known angles

$163^\circ + 109^\circ = 272^\circ$

Step2: Find sum of unknown angles

The total sum of angles in a quadrilateral is $360^\circ$.
$360^\circ - 272^\circ = 88^\circ$

Step3: Total parts of the ratio

The ratio is 3:5, so total parts = $3 + 5 = 8$

Step4: Calculate first unknown angle

Each part is $\frac{88^\circ}{8}=11^\circ$. First angle = $3 \times 11^\circ = 33^\circ$

Step5: Calculate second unknown angle

Second angle = $5 \times 11^\circ = 55^\circ$

Answer:

$33^\circ$ and $55^\circ$