The ratio of angles of a triangle is 7:2:1. Find the measure of the largest angle

Question

What is the measure of the largest angle

 

Answer 1

7x + 2x + x = 180 (this equation represents that the largest angle is 7 times that of the smallest angle, and the second largest angle is twice the measure of the smallest. we set this equal to 180 because the sum of the angles in a triangle is 180)

 

10X=180

      10

 

x=18 degrees is the measure of the smallest angle, however, the question asks about the largest angle.

The largest angle is given as 7x

 7(18) = 126

 

Let's check our answers:

7(18) + 2(18) + 18 = 180

126+36+18=180 degrees

Answer 2

Since the ratio of the angles is 7:2:1, we can write the angles as 7x, 2x, and x, for some x. Since the sum of the angles in a triangles is 180, we have 7x + 2x + x = 180. Combining the x's on the left-hand side, we have 10x = 180. Finally, dividing by 10 gives x = 18. Since the angles are 7x, 2x, and x, substituting 18 for x gives us 7*(18), 2*(18), and 18. Thus, the angles are 126, 36, and 18.

Answer 3

Howdy, Cameron. We meet again.

 

Since we have a ratio of 7:2:1, then we have 10 total parts.  How many degrees are in a triangle? 180, right?

 

If there are 10 parts, then each is 18 degrees. 180/10 = 18.

 

Since the largest angle is 7 parts, 7 x 18 = 126.

 

126 degrees is your answer.  The other two are 18 and 36 degrees.

 

Hope this helps!