Question

a quadrilateral has two angles that measure 234° and 80°. the other two angles are in a ratio of 10:13. what are the measures of those two angles?
□° and □°
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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: \(234^\circ + 80^\circ = 314^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(10x\) and \(13x\). Their sum is \(360^\circ - 314^\circ = 46^\circ\). So, \(10x + 13x = 46^\circ\).

Step4: Solve for x

Combine like terms: \(23x = 46^\circ\). Then, \(x = \frac{46^\circ}{23} = 2^\circ\).

Step5: Find the two angles

First angle: \(10x = 10\times2^\circ = 20^\circ\). Second angle: \(13x = 13\times2^\circ = 26^\circ\).

Answer:

\(20^\circ\) and \(26^\circ\)