Question

a quadrilateral has two angles that measure 266.3° and 80.5°. the other two angles are in a ratio of 14:19. 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

Add the two given angles: \(266.3^\circ + 80.5^\circ = 346.8^\circ\).

Step3: Find sum of unknown angles

Subtract the sum of known angles from \(360^\circ\): \(360^\circ - 346.8^\circ = 13.2^\circ\).

Step4: Set up ratio variables

Let the two unknown angles be \(14x\) and \(19x\) (since their ratio is \(14:19\)).

Step5: Solve for \(x\)

The sum of the unknown angles is \(14x + 19x = 33x\). We know this sum is \(13.2^\circ\), so \(33x = 13.2\). Solving for \(x\), we get \(x=\frac{13.2}{33}=0.4\).

Step6: Calculate the two angles

First angle: \(14x = 14\times0.4 = 5.6^\circ\). Second angle: \(19x = 19\times0.4 = 7.6^\circ\).

Answer:

\(5.6\)° and \(7.6\)°