Question

a triangle has an angle that measures 45°. the other two angles are in a ratio of 2:7. what are the measures of those two angles? o and o

Explanation:

Step1: Find the sum of the other two angles

The sum of angles in a triangle is \(180^{\circ}\). One angle is \(45^{\circ}\), so the sum of the other two angles is \(180 - 45=135^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(2:7\). Let the angles be \(2x\) and \(7x\). Then \(2x + 7x=135\), which simplifies to \(9x = 135\). Solving for \(x\), we get \(x=\frac{135}{9}=15\).

Step3: Calculate the two angles

For the first angle: \(2x = 2\times15 = 30^{\circ}\).
For the second angle: \(7x = 7\times15 = 105^{\circ}\).

Answer:

\(30\) and \(105\)