Question

Find the measure of angle A.​

Answer 1

30 degrees

Explanation:

Keep this in mind, ALL triangles must equal 180 degrees.

This is an acute triangle, hence one of the angles is 90 degrees. To find the other two angles, we must solve for x. Since we know the sum of all angles in this triangle must equal 180 degrees, we know for setting up our equation, all the angles should equal 180.

`90 + (x+37) + (x+67) = 180\\`

Now solve for x by isolating x

`2x + 194 = 180\\2x=-14\\x=-7`

Our x is -7, now that we know that the numerical value of x is -7, replace x with -7 for angle A.

-7 + 37 = 30

<A is 30 degrees.

Check your work

Plug in -7 where you see x.

`90 + (x+37) + (x+67) = 180\\90 + (-7+37) + (-7+67) = 180\\90 + 30 + 60 = 180\\180 = 180`

Turns out this was a 30-60-90 triangle. ✅