Triangles' angle A 4X as large as B. C is 20 less than B.

[personneedshelp]

In triangle ABC, the measure of angle A is four times as large as the measure of angle B. Angle C measures 20 degrees less than angle B. What is the measure of each angle?

I'm not sure by what "four times as large" means. Does that mean that if angle B is 30 degrees, then angle A would be 120 degrees or would angle A be 34 degrees? I'm having a hard time coming up with the answer, so could someone show me how to figure it out? :?

 

[Deleted member 4993]

Re: Triangles

In triangle ABC, the measure of angle A is four times as large as the measure of angle B. Angle C measures 20 degrees less than angle B. Find the measure of each angle.

I'm not sure by what "four times as large" means. Does that mean that if angle B is 30 degrees, then angle A would be 120 degrees or would angle A be 34 degrees?

It means if

angle B = 20[sup:qcpfbplp]o[/sup:qcpfbplp] ------- then-------- angle A = 4 * 20[sup:qcpfbplp]o[/sup:qcpfbplp] = 80[sup:qcpfbplp]o[/sup:qcpfbplp]

angle B = 30[sup:qcpfbplp]o[/sup:qcpfbplp] ------- then-------- angle A = 4 * 30[sup:qcpfbplp]o[/sup:qcpfbplp] = 120[sup:qcpfbplp]o[/sup:qcpfbplp]

 

[mmm4444bot]

… could someone show me how to figure it out?

Do you know that the three interior angles of any triangle add up to 180 degrees? This fact allows you to write an equation.

Since angles A and C are both stated in terms of angle B, we can write an equation to solve for B. Once we know the value of B, the values of A and C come naturally.



Here's an example exercise to show what I just wrote.

"In triangle ABC, angle B is 9 degrees more than 3 times the measure of angle A, and angle C is 86 degrees greater than the measure of angle A."

In this example, it is the measures of angles B and C that are both stated in terms of angle A, so we can write an equation to solve for A.

B = 3A + 9

C = A + 86

A + B + C = 180

A + 3A + 9 + A + 86 = 180

Solving this equation yields A = 17.

Naturally, we use this value to calculate B and C.

B = 3(17) + 9

C = 17 + 86



If you would like more help with your exercise, then please show whatever work you can, so that we might determine where to continue helping you.

 

[personneedshelp]

Re: Triangles

Thank you very much for all of your help! I really appreciate it.