Question

a quadrilateral has two angles that measure 283° and 35°. the other two angles are in a ratio of 8:13. 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: \(283^\circ + 35^\circ = 318^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(8x\) and \(13x\). Their sum is \(360^\circ - 318^\circ = 42^\circ\). So, \(8x + 13x = 42^\circ\).

Step4: Solve for \(x\)

Combine like terms: \(21x = 42^\circ\). Then, \(x = \frac{42^\circ}{21} = 2^\circ\).

Step5: Find the two angles

First angle: \(8x = 8\times2^\circ = 16^\circ\). Second angle: \(13x = 13\times2^\circ = 26^\circ\).

Answer:

\(16\) and \(26\)