Question

two angles of a quadrilateral measure 91° and 191°. the other two angles are in a ratio of 7:19. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the other two angles

The sum of the interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$. Let the sum of the two unknown - angled be $x$. Then $x=360-(91 + 191)=360 - 282=78^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be $7y$ and $19y$. Then $7y+19y = 78$. Combining like - terms, we get $26y = 78$.

Step3: Solve for $y$

Dividing both sides of the equation $26y = 78$ by 26, we have $y=\frac{78}{26}=3$.

Step4: Find the measures of the two angles

The first angle is $7y = 7\times3 = 21^{\circ}$, and the second angle is $19y=19\times3 = 57^{\circ}$.

Answer:

$21$ and $57$