Question

two angles of a quadrilateral measure 79° and 242°. the other two angles are in a ratio of 3:10. 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: \(79^\circ + 242^\circ = 321^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(3x\) and \(10x\). Their sum is \(3x + 10x = 13x\). Total sum of all angles is \(360^\circ\), so \(321^\circ + 13x = 360^\circ\). Solving for \(x\): \(13x = 360 - 321 = 39\), so \(x = \frac{39}{13} = 3\).

Step4: Find the unknown angles

First unknown angle: \(3x = 3\times3 = 9^\circ\). Second unknown angle: \(10x = 10\times3 = 30^\circ\). Wait, that can't be right. Wait, recalculate sum of known angles: \(79 + 242 = 321\)? No, \(79 + 242 = 321\)? Wait, \(79 + 242 = 321\)? Wait, \(79 + 240 = 319\), plus 2 is 321. Then \(360 - 321 = 39\). So \(3x + 10x = 13x = 39\), so \(x = 3\). Then angles are \(9\) and \(30\). But that seems small. Wait, maybe I made a mistake in angle sum? No, quadrilateral sum is \(360^\circ\). Wait, maybe the given angles are wrong? Wait, the problem says two angles are \(79^\circ\) and \(242^\circ\). \(79 + 242 = 321\), so remaining two angles sum to \(39\). Then ratio \(3:10\), so \(3x + 10x = 13x = 39\), \(x = 3\), so angles \(9\) and \(30\). Yes, that's correct.

Answer:

\(9\) and \(30\)