Question

a quadrilateral has two angles that measure 130° and 100°. the other two angles are in a ratio of 7:19. 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

Sum of given angles: \(130^\circ + 100^\circ = 230^\circ\).

Step3: Find sum of unknown angles

Let the unknown angles be \(7x\) and \(19x\). Their sum is \(360^\circ - 230^\circ = 130^\circ\). So, \(7x + 19x = 130^\circ\).

Step4: Solve for \(x\)

Combine like terms: \(26x = 130^\circ\). Then, \(x = \frac{130^\circ}{26} = 5^\circ\).

Step5: Find unknown angles

First angle: \(7x = 7\times5^\circ = 35^\circ\). Second angle: \(19x = 19\times5^\circ = 95^\circ\).

Answer:

\(35^\circ\) and \(95^\circ\)