Question

In right △ABC with right angle B, m∠A=(3x−8)° and m∠C=(x−2)°.

What is m∠A?

Question Options:


47°


67°


25°


92

Answer 1

67°

Explanation:

In a right triangle, the acute angles are complementary. That means that the sum of their measures is 90 deg.

m<A + m<C = 90

3x - 8 + x - 2 = 90

4x - 10 = 90

4x = 100

x = 25

m<A = 3x - 8

m<A = 3(25) - 8

m<A = 75 - 8

m<A = 67

Answer 2

<A = 67

Explanation:

The three angles of a triangle add up to 180 degrees. We know a right angle is 90 degrees.

<A + <B + <C = 180

3x-8 + 90 + x-2 =180

Combine like terms

4x-10+90 = 180

4x+80 =180

Subtract 80 from each side

4x+80-80=180-80

4x=100

Divide each side by 4

4x/4 = 100/4

x=25

But we want to know <A

<A = 3x-8

Substitute x=25

=3(25) -8

=75-8

= 67