The measure of angle 5 is 75°.
<u>Step-by-step explanation</u>:
Properties of intersecting lines :
- The angles formed opposite to each other at the point of intersection are called vertically opposite angles.
- These vertically opposite angles are congruent (same).
step 1 :
From the figure, the angle (-9x-12) and angle (6x+183) are vertically opposite and are equal.
-9x-12 = 6x+183
⇒ -9x-6x = 183+12
⇒ -15x = 195
⇒ x = -(195/15) = -13
step 2 :
Substitute x= -13 in the angle (-9x-12)
⇒ (-9x-12) = -9(-13)-12
⇒ 117 - 12 = 105°
step 3 :
<em>The measure of angle in a line is supplementary (180°)</em>.
<em>Let angle 5 be unknown value "a"</em>.
Then, angle (-9x-12) + angle a = 180°
⇒ 105° + a = 180°
⇒ a = 180 - 105
⇒ a = 75°
∴ The measure of angle 5 is 75°
