Question

Find x.
Finding an angle measure given extended triangles.

Answer 1

Answer is x= 58

Step by step

We know

The sum of the angles in the triangle = 180
The sum of a straight angle = 180
Vertical angles are congruent

First I found the adjacent angle to the known angle 92 in the straight angle. 180 - 92 = 88

Now we have 2 known angles in the triangle, 88 and 34. We subtract these from 180 to find the third angle.
180 - 88 - 34 = 58

Angle x is a vertical angle to 58 so angle x = 58

See attachment for help.

Problem solved!

Answer 2

60

Explanation:

180-92=88

angles on a strait line add up to 180

34+88+x=180

120+x=180

180-120=x

x=60

alternate angles

angles in triangle add up to 180