Question

I need to find the value of x in this figure. I need to do it so that whatever x is, it can be substituted into the expressions

Remember: all the angles of a triangle = 180 degrees and other geometry stuff
please help :)

Answer 1

x = 42

see below for the angle measures.

Explanation:

The angle marked 2x - 9 is sort of outside the triangle. It is called an exterior angle. The other two angles are called remote interior angles. "Remote" means that they are away from the exterior angle. When you have this set up, the two remote angles added together EQUAL the exterior one.

x+5 + 28 = 2x - 9

x + 33 = 2x - 9

Subtract x.

33 = x - 9

Add 9.

42 = x

So x = 42° which if you put that back into the expressions you can find the measures of the one remote interior angle (the other we know is 28°) and the exterior angle.

remote int angle:

x+5

= 42 + 5

= 47°

Exterior angle:

2x - 9

= 2(42) - 9

= 84 - 9

= 75°

(You can also then find the completely unmarked angle which is 180°- 75° which is 105°)