Question

M<1=
What is the measure of <1?
1
(5x − 2)°
(8x + 1)º

Answer 1

m<1 = 147°

Explanation:

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

Given the small right angle, which lies to the right of the triangle, we know that the straight line splitting the right angle and the triangle is a perpendicular bisector. This means that the final angle in the triangle is a right angle.

Thus, we can use this formula to find x:

`5x-2+8x+1+90=180\\13x+89=180\\13x=91\\x=7`

By plugging in 7 for x in the angle beside <1 we find that it measures 5(7)-2 = 33°

We know that this angle and angle 1 are supplementary angles and the sum of the two angles must equal 180°.

So we can simply subtract 33 from 180 to find m<1:

`180-33=147`