Question

two angles of a quadrilateral measure 296.9° and 48.6°. the other two angles are in a ratio of 14:15. what are the measures of those two angles? \\(\square\\)° and \\(\square\\)°

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: \(296.9^\circ + 48.6^\circ = 345.5^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(14x\) and \(15x\). Their sum is \(360^\circ - 345.5^\circ = 14.5^\circ\).

Step4: Solve for \(x\)

\(14x + 15x = 14.5\)
\(29x = 14.5\)
\(x = \frac{14.5}{29} = 0.5\).

Step5: Find the angles

First angle: \(14x = 14 \times 0.5 = 7^\circ\).
Second angle: \(15x = 15 \times 0.5 = 7.5^\circ\).

Answer:

\(7\)° and \(7.5\)°