Question

two angles of a quadrilateral measure 296° and 15°. the other two angles are in a ratio of 3:4. 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 $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Calculate the sum of the two unknown angles.

Let the sum of the two unknown angles be $x$. We know two angles are $296^{\circ}$ and $15^{\circ}$. So $x=360-(296 + 15)=360 - 311=49^{\circ}$.

Step3: Use the ratio to find the individual angles.

The two angles are in the ratio $3:4$. Let the angles be $3y$ and $4y$. Then $3y + 4y=49$, so $7y = 49$, and $y=\frac{49}{7}=7$.
The first angle is $3y = 3\times7 = 21^{\circ}$, and the second angle is $4y=4\times7 = 28^{\circ}$.

Answer:

$21$ and $28$