Question

a triangle has an angle that measures 45°. the other two angles are in a ratio of 10:17. 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 \(45^{\circ}\), 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 \(10:17\). Let the angles be \(10x\) and \(17x\). Then \(10x + 17x=135\), \(27x = 135\), \(x=\frac{135}{27}=5\)

Step3: Calculate the two angles

For the first angle: \(10x = 10\times5 = 50^{\circ}\)
For the second angle: \(17x=17\times 5=85^{\circ}\)

Answer:

\(50\) and \(85\)