Question

choose the most appropriate letter. show work
1)
in the figure above, if ab is a line, what is the value of y?
(a) 108
(b) 114
(c) 117
(d) 120
(e) 135
2)
ab = 180

Explanation:

Step1: Count x angles on one side

There are 6 $x^\circ$ angles on half of line AB.

Step2: Set up equation for straight line

A straight line is $180^\circ$, so:
$$6x = 180$$

Step3: Solve for x

Calculate x by dividing:
$$x = \frac{180}{6} = 30$$

Step4: Relate y and x to straight line

$y + 2x = 180$ (they form a straight line).

Step5: Substitute x to find y

Plug $x=30$ into the equation:
$$y + 2(30) = 180$$
$$y + 60 = 180$$
$$y = 180 - 60 = 117$$

Answer:

C) 117