Question

two angles of a quadrilateral measure 142° and 126°. the other two angles are in a ratio of 3:20. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the four - angle measures of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Calculate the sum of the two unknown angles

Let the sum of the two unknown angles be $x$. We know two angles are $142^{\circ}$ and $126^{\circ}$. So $x = 360-(142 + 126)=360 - 268=92^{\circ}$.

Step3: Use the ratio to find the individual angles

The two angles are in the ratio $3:20$. Let the common multiplier be $k$. Then the two angles are $3k$ and $20k$. And $3k+20k=92$, so $23k = 92$. Solving for $k$, we get $k=\frac{92}{23}=4$.
The first unknown angle is $3k = 3\times4 = 12^{\circ}$.
The second unknown angle is $20k=20\times4 = 80^{\circ}$.

Answer:

$12$ and $80$