The angles in a right triangle form an arithmetic progression. If the smallest angle is 13 degrees, then what is the largest angle?

Guest Aug 29, 2021

#1**0 **

*The angles in a right triangle form an arithmetic progression. If the smallest angle is 13 degrees, then what is the largest angle?*

An arithmetic progression means you get them by addition. So,

Let the 1st angle be called (13)

Let the 2nd angle be called (13 + D) D for difference

Let the 3rd angle be called (13 + D + D)

We know that the sum of all three angles of a triangle is 180

(13) + (13 + D) + (13 + D + D) = 180

39 + 3D = 180

3D = 180 – 39 = 141

D = 141 / 3 = 47

Thus

The 1st angle = 13

The 2nd angle = (13 + 47) = 60

The 3rd angle = (13 + 47 + 47) = **107 degrees**

Check: 13 + 60 + 107 = 180

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Guest Aug 29, 2021

#2**0 **

*The angles in a right triangle form an arithmetic progression. If the smallest angle is 13 degrees, then what is the largest angle?*

It's me again. I just re-read the question. I overlooked that it says **right triangle**. Disregard answer #1.

So one angle of a right triangle is 90 degrees.

Since the other two angles have to total the other 90 degrees, each of them is less than 90 degrees.

Therefore the largest angle is **90 degrees**.

BTW, it's not necessary to determine the arithmetic progression, if there is one.

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Guest Aug 29, 2021