Question

1. a quadrilateral has two angles that measure 100° and 60°. the other angles have a ratio of 3:7. what are the measures of those angles?

Explanation:

Step1: Calculate sum of unknown angles

The total interior angle sum of a quadrilateral is $360^\circ$. Subtract the known angles:
$360^\circ - 100^\circ - 60^\circ = 200^\circ$

Step2: Define variables for ratio parts

Let the ratio parts be $3x$ and $17x$. Set their sum equal to $200^\circ$:
$3x + 17x = 200^\circ$

Step3: Solve for $x$

Combine like terms and isolate $x$:
$20x = 200^\circ$
$x = \frac{200^\circ}{20} = 10^\circ$

Step4: Find each unknown angle

Calculate the value of each ratio part:
First angle: $3x = 3 \times 10^\circ = 30^\circ$
Second angle: $17x = 17 \times 10^\circ = 170^\circ$

Answer:

The measures of the angles are $30^\circ$ and $170^\circ$.