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:

m = 19°

(3m)° = 57°

(2m-5)° = 33°

Step-by-step explanation:

From the figure attached below,

Let’s assume that in right-angled ∆ABC, we have  

Angle B = 90°

Angle A = (3m)°

Angle C = (2m-5)°

Since we know that, according to the angle sum property, the sum of angles of a triangle is equal to 180°.

Therefore, we have  

∠A + ∠B + ∠C = 180°

⇒ (3m)° + (2m-5)° + 90° = 180°

⇒ (3m)° + (2m-5)° = 180° - 90°

⇒ (3m)° + (2m-5)° = 90°

⇒ (3m + 2m) ° = 90° + 5°

⇒ 5m° = 95°

⇒ m = 95° / 5°  

⇒ m = 19°

Now,  

The two smallest interior angles of the right-angled triangle ABC will be as follows:

∠A = (3m)° = 3 * 19° = 57°

∠C = (2m-5)° = 2*19° - 5 = 33°

Answer 2

Answer:

m=19°,B=57° and C=33°

Step-by-step explanation:

In a right angle triangle sum of all angles is equal to 180°  and One angle is 90°

let A B and C are 3 angles

Angle A = 90°

Angle B = (3m)°

Angle C = (2m-5)°

Sum of angles=180°

∠A + ∠B + ∠C = 180°

90°+(3m)° + (2m-5)° = 180°

(3m)° + (2m-5)° = 180° - 90°

3m° + 2m°-5° = 90°

3m° + 2m° = 90° + 5°

5m° = 95°

m = 95° / 5°  

m = 19° is answer

Now,  

Put the value of m in the B & C

∠B = (3m)° = 3 * 19° = 57° is answer

∠C = (2m-5)° = 2*19° - 5 = 33° is answer

now for our checking that our answer is right or wrong

∠A+∠B+∠C=180°

90°+57°+33°=180°

180°=180° proved So our answer is Right