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.
Answers
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:
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