Question

1. two angles of a quadrilateral measure 160° and 10°. the others are at a ratio of 2:7. what are their measures?

Explanation:

Step1: Find sum of unknown angles

The total interior angle sum of a quadrilateral is $360^\circ$. Subtract the known angles:
$360^\circ - 160^\circ - 10^\circ = 190^\circ$

Step2: Define variables for ratio

Let the unknown angles be $2x$ and $17x$ (matching the ratio 2:17).

Step3: Solve for $x$

Set the sum equal to $190^\circ$:
$2x + 17x = 190^\circ$
$19x = 190^\circ$
$x = \frac{190^\circ}{19} = 10^\circ$

Step4: Calculate each unknown angle

First angle: $2x = 2 \times 10^\circ = 20^\circ$
Second angle: $17x = 17 \times 10^\circ = 170^\circ$

Answer:

The measures of the two angles are $20^\circ$ and $170^\circ$.