Question

in a right triangle, the acute angles measure x+15 and 2x degrees. what is the measure of the larger acute angle of the triangle?
○ 40
○ 50
○ 15
○ 25

Explanation:

Step1: Recall right triangle angle sum

In a right triangle, the two acute angles sum to \(90^\circ\) (since one angle is \(90^\circ\) and the total sum of angles in a triangle is \(180^\circ\)). So, we set up the equation: \((x + 15)+2x=90\).

Step2: Solve for \(x\)

Combine like terms: \(3x + 15 = 90\). Subtract 15 from both sides: \(3x=90 - 15=75\). Divide both sides by 3: \(x=\frac{75}{3}=25\).

Step3: Find the two acute angles

First angle: \(x + 15=25 + 15 = 40^\circ\). Second angle: \(2x=2\times25 = 50^\circ\).

Step4: Identify the larger angle

Compare \(40^\circ\) and \(50^\circ\); the larger one is \(50^\circ\).

Answer:

50