Question

The two smallest interior angles of a right triangle have measures of (3m)° and (2m – 5)°.

What is the value of m? Show your work, and explain your reasoning.

Answer 1

Answer:

The value of m is 19° and the angles are 57° & 33°.

Step-by-step explanation:

By Angle sum property, take the sum of 3 angles (3m)°, (2m-5)° & 90°

-> 3m + (2m-5) + 90° = 180°

-> 3m + 2m - 5 = 180 - 90

-> 5m - 5 = 90

-> 5m = 90 + 5

-> m = $</strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>\frac</strong><strong>{95}{5</strong><strong>}</strong><strong>}</strong><strong>$

$\boxed{m = 19°}$

The two interior angles are :

(3m)° = 3 × 19 = 57°

(2m - 5)° = 2 × 19 - 5 = 33°