Question

a triangle has an angle that measures 15°. the other two angles are in a ratio of 4:7. what are the measures of those two angles?
and
°

Explanation:

Step1: Find the sum of the other two angles

The sum of angles in a triangle is \(180^{\circ}\). One angle is \(15^{\circ}\), so the sum of the other two angles is \(180 - 15=165^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(4:7\). Let the angles be \(4x\) and \(7x\). Then \(4x + 7x=165\), which simplifies to \(11x = 165\). Solving for \(x\), we get \(x=\frac{165}{11}=15\).

Step3: Calculate the two angles

For the first angle: \(4x = 4\times15 = 60^{\circ}\).
For the second angle: \(7x = 7\times15 = 105^{\circ}\).

Answer:

\(60\) and \(105\)