Question

Help with this problem. thanks.

Answer 1

The correct answer is: Option (B) m∠a = 38°, m∠b = 52°, m∠c = 90°

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).