Question

a quadrilateral has two angles that measure 70° and 140°. the other two angles are in a ratio of 7:8. 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 $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Calculate the sum of the other two angles

Let the sum of the other two angles be $x$. We know two angles are $70^{\circ}$ and $140^{\circ}$, so $x=360-(70 + 140)=360 - 210=150^{\circ}$.

Step3: Use the ratio to find the individual angles

The two angles are in the ratio $7:8$. Let the angles be $7y$ and $8y$. Then $7y+8y = 150$, so $15y=150$, and $y = 10$.
The first angle is $7y=7\times10 = 70^{\circ}$, and the second angle is $8y=8\times10=80^{\circ}$.

Answer:

$70$ and $80$