Question

one angle of a triangle measures 80°. the other two angles are in a ratio of 3:7. 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 \(80^{\circ}\), so the sum of the other two angles is \(180 - 80=100^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(3:7\). Let the angles be \(3x\) and \(7x\). Then \(3x + 7x=100\), which simplifies to \(10x = 100\), so \(x = 10\).
For the first angle: \(3x=3\times10 = 30^{\circ}\)
For the second angle: \(7x=7\times10 = 70^{\circ}\)

Answer:

\(30\) and \(70\)