Question

If angle a of a triangle is x, angle b is 2x, and angle c is (3/4)x, then what is the measure of angle b. In the problem, I need to solve how angle b is equal to 96 degrees. The 96 was a given but how do I solve that to firgure it out using a two column proof?

Answer 1

Given:

Angle a of a triangle is x, angle b is 2x, and angle c is (3/4)x.

To find:

The measure of angle b.

Solution:

The two column proof is

Statement Reason

1.
`\angle a=x,\angle b=2x,\angle c=(3)/(4)x` 1. Given

2.
`x+2x+(3)/(4)x=180^\circ` 2. Angle sum property

3.
`(15)/(4)x=180^\circ` 3. Combining like terms

4.
`15x=720^\circ` 4. Multiplying both sides by 4.

5.
`x=48^\circ` 5. Dividing both sides by 15.

6.
`m\angle b=2x=2(48^\circ)=96^\circ` 6. On substituting the value of x in 2x.

Therefore, the measure of angle b is 96°.