Questions: Find the measure of angles a-g in the figure. Assume that L1 and L2 are parallel and that m is an intersec

Transcript text: Find the measure of angles $a-g$ in the figure. Assume that $L_{1}$ and $L_{2}$ are parallel and that $m$ is an intersec

Solution

Solution Steps

Step 1: Identify the given angle

The given angle is $ \angle a = 140^\circ $.

Step 2: Find the corresponding angle

Since $ L_1 $ and $ L_2 $ are parallel and $ m $ is a transversal, the corresponding angle to $ \angle a $ is $ \angle e $. Therefore, $ \angle e = 140^\circ $.

Step 3: Find the alternate interior angle

The alternate interior angle to $ \angle a $ is $ \angle c $. Since alternate interior angles are equal, $ \angle c = 140^\circ $.

Step 4: Find the supplementary angle

The angle $ \angle b $ is supplementary to $ \angle a $. Therefore, $ \angle b = 180^\circ - 140^\circ = 40^\circ $.

Step 5: Find the corresponding angle to $ \angle b $

The corresponding angle to $ \angle b $ is $ \angle f $. Therefore, $ \angle f = 40^\circ $.

Step 6: Find the alternate interior angle to $ \angle b $

The alternate interior angle to $ \angle b $ is $ \angle g $. Therefore, $ \angle g = 40^\circ $.

Step 7: Find the vertical angle to $ \angle e $

The vertical angle to $ \angle e $ is $ \angle d $. Therefore, $ \angle d = 140^\circ $.

Final Answer

$ \angle a = 140^\circ $
$ \angle b = 40^\circ $
$ \angle c = 140^\circ $
$ \angle d = 140^\circ $
$ \angle e = 140^\circ $
$ \angle f = 40^\circ $
$ \angle g = 40^\circ $

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!