Question

a quadrilateral has two angles that measure 167° and 117°. the other two angles are in a ratio of 3:16. what e the measures of those two angles? ° and °

Explanation:

Step1: Sum known angles

$167^\circ + 117^\circ = 284^\circ$

Step2: Find remaining angle sum

The total interior angle sum of a quadrilateral is $360^\circ$.
$360^\circ - 284^\circ = 76^\circ$

Step3: Define ratio variables

Let the angles be $3x$ and $16x$.
$3x + 16x = 76^\circ$

Step4: Solve for $x$

$19x = 76^\circ$
$x = \frac{76^\circ}{19} = 4^\circ$

Step5: Calculate unknown angles

First angle: $3x = 3 \times 4^\circ = 12^\circ$
Second angle: $16x = 16 \times 4^\circ = 64^\circ$

Answer:

$12^\circ$ and $64^\circ$