Question

two angles of a quadrilateral measure 230° and 60°. the other two angles are in a ratio of 2:5. 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: \(230^\circ\) and \(60^\circ\). Their sum is \(230 + 60 = 290^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(2x\) and \(5x\) (since ratio is \(2:5\)). The sum of all angles is \(360^\circ\), so \(290 + 2x + 5x = 360\). Simplify: \(290 + 7x = 360\).

Step4: Solve for \(x\)

Subtract \(290\) from both sides: \(7x = 360 - 290 = 70\). Then \(x = \frac{70}{7} = 10\).

Step5: Find unknown angles

First angle: \(2x = 2\times10 = 20^\circ\). Second angle: \(5x = 5\times10 = 50^\circ\).

Answer:

\(20^\circ\) and \(50^\circ\)