Question

a quadrilateral has two angles that measure 110° and 130°. the other two angles are in a ratio of 5:7. 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: \(110^\circ + 130^\circ = 240^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(5x\) and \(7x\). Their sum is \(360^\circ - 240^\circ = 120^\circ\). So, \(5x + 7x = 120^\circ\).

Step4: Solve for \(x\)

Combine like terms: \(12x = 120^\circ\). Divide both sides by 12: \(x = 10^\circ\).

Step5: Find the two angles

First angle: \(5x = 5\times10^\circ = 50^\circ\). Second angle: \(7x = 7\times10^\circ = 70^\circ\).

Answer:

\(50\) and \(70\)