Question

two angles of a quadrilateral measure 47° and 279°. the other two angles are in a ratio of 6:11. what are the measures of those two angles? ° and °

Explanation:

Step1: Sum of known angles

$47^\circ + 279^\circ = 326^\circ$

Step2: Find sum of unknown angles

The total sum of interior angles of a quadrilateral is $360^\circ$.
$360^\circ - 326^\circ = 34^\circ$

Step3: Define variables for ratio

Let the angles be $6x$ and $11x$.
$6x + 11x = 34^\circ$

Step4: Solve for x

$17x = 34^\circ$
$x = \frac{34^\circ}{17} = 2^\circ$

Step5: Calculate each unknown angle

First angle: $6 \times 2^\circ = 12^\circ$
Second angle: $11 \times 2^\circ = 22^\circ$

Answer:

$12^\circ$ and $22^\circ$