AB and CD are parallel lines and EH is a transversal. The size of angle EFB is (2x - 100)° and the size of angle CGF is (x + 52)°. What is the actual size of the angle EFB ?
Answers
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:
The actual size of the ∠EFB is 52°.
Step-by-step explanation:
Given AB and CD are parallel lines, EH is a transversal.
Also ∠EFB = (2x-100)°, ∠CGF = (x+52)°
Pair of corresponding angles:
A pair of corresponding angles are a pair of angles in which one arm of each angle is on the same side of the transversal and their other arms are headed in the same direction.
From the figure,
- ∠EFB and ∠FGD are Pair of corresponding angles.
So, ∠EFB = ∠FGD = (2x-100)°
- ∠CGF and ∠FGD are the linear pair.
∠CGF + ∠FGD = 180°
(x+52)°+(2x-100)°= 180°
3x - 48° = 180°
3x = 228°
x = 76°
- Now substitute x = 76° in ∠EFB = (2x-100)°
∠EFB = (2x-100)°
= (2(76°)-100°)
∠EFB = 52°
Hence the actual size of ∠EFB = 52°.
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