Question

a quadrilateral has two angles that measure 205° and 85°. the other two angles are in a ratio of 3:4. 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

Known angles: \(205^\circ\) and \(85^\circ\). Their sum is \(205 + 85 = 290^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles sum to \(x\). Then \(x = 360 - 290 = 70^\circ\).

Step4: Use ratio to find each angle

The ratio of the two unknown angles is \(3:4\). Let the angles be \(3k\) and \(4k\). Then \(3k + 4k = 70\), so \(7k = 70\), \(k = 10\). Thus, the angles are \(3\times10 = 30^\circ\) and \(4\times10 = 40^\circ\).

Answer:

\(30^\circ\) and \(40^\circ\)