Question

two angles of a quadrilateral measure 277° and 45°. the other two angles are in a ratio of 5:14. 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

Known angles: \(277^\circ\) and \(45^\circ\). Their sum is \(277 + 45 = 322^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles sum be \(x\). Then \(x = 360 - 322 = 38^\circ\).

Step4: Set up ratio equation

Let the two unknown angles be \(5k\) and \(14k\). So \(5k + 14k = 38\).

Step5: Solve for k

\(19k = 38\) ⇒ \(k = 2\).

Step6: Find the angles

First angle: \(5k = 5\times2 = 10^\circ\). Second angle: \(14k = 14\times2 = 28^\circ\).

Answer:

\(10\) and \(28\)