Question

two angles of a quadrilateral measure 214.5° and 122.7°. the other two angles are in a ratio of 6:13. what are the measures of those two angles?
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Explanation:

Step1: Recall quadrilateral angle sum

The sum of interior angles of a quadrilateral is \(360^\circ\).

Step2: Calculate sum of known angles

Sum of given angles: \(214.5^\circ + 122.7^\circ = 337.2^\circ\)

Step3: Find sum of unknown angles

Let the unknown angles be \(6x\) and \(13x\). Their sum is \(360^\circ - 337.2^\circ = 22.8^\circ\)

Step4: Solve for \(x\)

\(6x + 13x = 22.8^\circ\)
\(19x = 22.8^\circ\)
\(x = \frac{22.8^\circ}{19} = 1.2^\circ\)

Step5: Find the two angles

First angle: \(6x = 6\times1.2^\circ = 7.2^\circ\)
Second angle: \(13x = 13\times1.2^\circ = 15.6^\circ\)

Answer:

\(7.2^\circ\) and \(15.6^\circ\)