Question

a quadrilateral has two angles that measure 215° and 65°. the other two angles are in a ratio of 7:9. what are the measures of those two angles?
□° and □°
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Explanation:

Step1: Recall quadrilateral angle sum

The sum of interior angles in a quadrilateral is \(360^\circ\).

Step2: Calculate sum of known angles

Add the two given angles: \(215^\circ + 65^\circ = 280^\circ\).

Step3: Find sum of unknown angles

Subtract the sum of known angles from \(360^\circ\): \(360^\circ - 280^\circ = 80^\circ\).

Step4: Set up ratio equation

Let the two unknown angles be \(7x\) and \(9x\). Then \(7x + 9x = 80^\circ\).

Step5: Solve for \(x\)

Combine like terms: \(16x = 80^\circ\), so \(x = \frac{80^\circ}{16} = 5^\circ\).

Step6: Find the angles

Calculate \(7x = 7\times5^\circ = 35^\circ\) and \(9x = 9\times5^\circ = 45^\circ\).

Answer:

\(35^\circ\) and \(45^\circ\)