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. $\angle a=x,\angle b=2x,\angle c=\dfrac{3}{4}x$                  1. Given

2. $x+2x+\dfrac{3}{4}x=180^\circ$                          2. Angle sum property

3. $\dfrac{15}{4}x=180^\circ$                                        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°.