Question

a quadrilateral has two angles that measure 323° and 9°. the other two angles are in a ratio of 5:9. what are the measures of those two angles?
□° and □°

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: \(323^\circ + 9^\circ = 332^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(5x\) and \(9x\). Then \(5x + 9x + 332^\circ = 360^\circ\). Simplify: \(14x = 360 - 332 = 28\).

Step4: Solve for x

\(x = \frac{28}{14} = 2\).

Step5: Find unknown angles

First angle: \(5x = 5\times2 = 10^\circ\). Second angle: \(9x = 9\times2 = 18^\circ\). Wait, no—wait, 323 + 9 is 332, 360 - 332 is 28? Wait, that can't be, 323 is too large for a quadrilateral angle (since angles in a quadrilateral must be less than 180? No, wait, no—wait, a quadrilateral can have reflex angles (greater than 180), but 323 is a reflex angle. Wait, but 323 + 9 is 332, so the remaining two angles sum to 28. Then ratio 5:9, so 5x + 9x = 14x = 28, x=2. So 10 and 18. Wait, but 323 is a valid angle (reflex), so that's correct.

Answer:

\(10^\circ\) and \(18^\circ\)