Question

Find the measure of angle 5. Will someone please help me. I have to answer this one question before I can move on to another one. Please help

Answer 1

The measure of angle 5 is 75°.

Step-by-step explanation:

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 :

The measure of angle in a line is supplementary (180°).

Let angle 5 be unknown value "a".

Then, angle (-9x-12) + angle a = 180°

⇒ 105° + a = 180°

⇒ a = 180 - 105

⇒ a = 75°

∴  The measure of angle 5 is 75°