Question

a quadrilateral has two angles that measure 342.1° and 7.1°. the other two angles are in a ratio of 7:20. what are the measures of those two angles?

Explanation:

Step1: Find the sum of the two known angles

$342.1^{\circ}+7.1^{\circ}=349.2^{\circ}$

Step2: Find the sum of the other two angles

The sum of the interior - angles of a quadrilateral is $360^{\circ}$. So the sum of the other two angles is $360^{\circ}-349.2^{\circ}=10.8^{\circ}$

Step3: Set up an equation based on the ratio

Let the two angles be $7x$ and $20x$. Then $7x + 20x=10.8^{\circ}$, which simplifies to $27x = 10.8^{\circ}$

Step4: Solve for $x$

$x=\frac{10.8^{\circ}}{27}=0.4^{\circ}$

Step5: Find the measures of the two angles

The first angle is $7x = 7\times0.4^{\circ}=2.8^{\circ}$
The second angle is $20x=20\times0.4^{\circ}=8^{\circ}$

Answer:

$2.8^{\circ}$ and $8^{\circ}$