Question

AB and CD are parallel lines and EH is a transversal.
What is the size of angle EFB?

Answer 1

Answer:

Hence, actual measure of <EFB = 52°

Step - by - step explanation :

Given,

< CGF = (x + 52)°

< EFB = (2x - 100) °

Then,

(x + 52) ° + (2x + 100) ° = 180°

=> x + 52 + 2x - 100 = 180°

=> 3x + 52° - 100° = 180°

=> 3x = 180° - 52° + 100°

=> 3x = 228°

=> x = 228/3 = 76

So, x = 76°

Now,

<EFB = 2x - 100 = 2(76) - 100 = 152 - 100 = 52°

Hence, actual measure of <EFB = 52°

Answer 2

Answer:

Concept:

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

Step-by-step explanation:

Given:

AB and CD are parallel lines and EH is a transversal.
Find:

What is the size of angle EFB
Solution:

Refer to the image attached

               $Given, \ \angle H G D=54^{\circ} \\\\ \angle \mathrm{GFB}=\angle \mathrm{HGD}=54^{\circ} (Corresponding angles)\\\\ \angle G F B+\angle E F B=180^{\circ} (Linear Pair)\\\\ 54^{\circ}+\angle E F B=180^{\circ} \\\\ \angle E F B=180^{\circ}-54^{\circ} \\\\ \therefore \angle E F B=126^{\circ}$

     The size of angle EFB is 126°

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