Question

What are the numerical measures of each angle in the

diagram?
<1 and 23 measure
degrees
22 and 24 measure
degrees
(3x - 1)
73
(2x + 9)

Answer 1

`m\angle 1\:and\:m\angle 3=29\degree`

`m\angle 2\:and\:m\angle 4=151\degree`

Explanation:

The missing diagram is shown in the attachment.

Recall that vertical angles are congruent:

`\implies 2x+9=3x-1`

`\implies 3x-2x=9+1`

`\therefore x=10`

`m\angle 1=m\angle 3=3(10)-1=30-1=29\degree`

The sum of angles on a straight line is 180 degrees

`m\angle 2=m\angle 4=180-29\degree=151\degree`