Question

a quadrilateral has two angles that measure 259° and 23°. the other two angles are in a ratio of 2:11. what are the measures of those two angles? ° and °

Explanation:

Step1: Sum of known angles

$259^\circ + 23^\circ = 282^\circ$

Step2: Find remaining angle sum

The total interior angle sum of a quadrilateral is $360^\circ$.
$360^\circ - 282^\circ = 78^\circ$

Step3: Define ratio variables

Let the angles be $2x$ and $11x$.
$2x + 11x = 78^\circ$

Step4: Solve for $x$

$13x = 78^\circ$
$x = \frac{78^\circ}{13} = 6^\circ$

Step5: Calculate the two angles

First angle: $2x = 2\times6^\circ = 12^\circ$
Second angle: $11x = 11\times6^\circ = 66^\circ$

Answer:

$12^\circ$ and $66^\circ$