Question

two angles of a quadrilateral measure 326° and 20°. the other two angles are in a ratio of 2:5. what are the measures of those two angles?

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 that two angles are $326^{\circ}$ and $20^{\circ}$. So $x = 360-(326 + 20)=360 - 346=14^{\circ}$.

Step3: Set up an equation based on the ratio

The two angles are in a ratio of $2:5$. Let the two angles be $2y$ and $5y$. Then $2y+5y=14$, which simplifies to $7y = 14$.

Step4: Solve for $y$

Dividing both sides of $7y = 14$ by 7, we get $y=\frac{14}{7}=2$.

Step5: Find the measures of the two angles

The first angle is $2y = 2\times2 = 4^{\circ}$, and the second angle is $5y=5\times2 = 10^{\circ}$.

Answer:

$4$ and $10$