Question

two angles of a quadrilateral measure 70° and 120°. the other two angles are in a ratio of 8:9. what are the measures of those two angles?\boxed{}° and \boxed{}°

Explanation:

Step1: Sum known angles

$70^\circ + 120^\circ = 190^\circ$

Step2: Find remaining angle sum

The total sum of interior angles in a quadrilateral is $360^\circ$.
$360^\circ - 190^\circ = 170^\circ$

Step3: Define ratio variables

Let the angles be $8x$ and $9x$.
$8x + 9x = 170^\circ$

Step4: Solve for x

$17x = 170^\circ$
$x = \frac{170^\circ}{17} = 10^\circ$

Step5: Calculate each unknown angle

First angle: $8x = 8 \times 10^\circ = 80^\circ$
Second angle: $9x = 9 \times 10^\circ = 90^\circ$

Answer:

$80^\circ$ and $90^\circ$