The correct answer is: Option (B) m∠a = 38°, m∠b = 52°, m∠c = 90°
Step-by-step explanation:
Given measure of each angle:
m∠a = (48-x)°
m∠b = (9x-38)°
m∠c = 90°
Now, as you can see, that one angle, m∠C, of the triangle ABC is 90°; therefore, we can infer that it is a right-angled triangle.
For right-angled triangle, the sum of all the angles is 180°. We can write it mathematically as:
m∠a + m∠b + m∠c = 180° --- (1)
Plug in all the measure of angles in equation (1):
(1)=> (48-x)° + (9x-38)° + 90° = 180°
Solve to find the value of x:
8x + 100° = 180°
8x = 80°
x = 10°
Now put the value of x in all individual angles to find m∠a, m∠b, and m∠c.
m∠a = (48-10)° = 38°
m∠b = (9*10-38)° = 52°
m∠c = 90°
Hence the correct answer is Option (B).