Question

two angles of a quadrilateral measure 177° and 120°. the other two angles are in a ratio of 5:16. 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: \(177^\circ + 120^\circ = 297^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(5x\) and \(16x\). Their sum is \(360^\circ - 297^\circ = 63^\circ\). So, \(5x + 16x = 63^\circ\).

Step4: Solve for \(x\)

Combine like terms: \(21x = 63^\circ\). Then, \(x = \frac{63^\circ}{21} = 3^\circ\).

Step5: Find the two angles

First angle: \(5x = 5\times3^\circ = 15^\circ\). Second angle: \(16x = 16\times3^\circ = 48^\circ\).

Answer:

\(15^\circ\) and \(48^\circ\)