Question

In a triangle, the measure of the second angle is twice the measure of the first angle. the third angel is equal to the sum of the other angels

Answer 1

So the angles have measurements 30,60, and 90 degrees.

Explanation:

We have a triangle which means the interior angles of that triangle has sum 180 degrees.

Let's call the angle measurements: A, B, and C.

A+B+C=180

B=2A (The second angle is twice the first.)

C=A+B (The third angle is the sum of the other 2.)

If C=A+B, then C=A+2A (since B=2A).

So we have this system:

A+B+C=180

B=2A

C=3A (since C=A+2A=3a).

Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:

A+B+C=180 with B=2A and C=3A.

A+2A+3A=180

6A=180

Divide both sides by 6:

A=180/6

A=30

If B=2A and A=30, then B=2(30)=60.

If C=3A and A=30, then C=3(30)=90.

So the angles have measurements 30,60, and 90 degrees.