☰
✕

Lines and Angles
Question
Wired Faculty App

In figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.

Answer

(i) ∠AGE = ∠GED = 126°
| Alternate Interior Angles
(ii)    ∠GED = 126°
⇒ ∠GEF + ∠FED = 126°
⇒ ∠GEF + 90° = 126°
| ∵ EF ⊥ CD ∴ ∠FED = 90°
⇒    ∠GEF = 126° - 90° = 36°
(iii) ∠GEC    + ∠GEF + ∠FED = 180°
| ∵ CD is a line
⇒ ∠GEC + 36° + 90° = 180°
⇒    ∠GEC + 126°= 180°
⇒    ∠GEC = 180° - 126° = 54°
Now,    ∠FGE = ∠GEC = 54°
| Alternate Interior Angles

Sponsor Area

Some More Questions From Lines and Angles Chapter

If the complement of an angle is one-third of its supplement, find the angle. 

In figure, find the value of x.

In figure, if ∠POR and ∠QOR form a linear pair and a - b = 80° then find the value of a and b.

What value of x would make XOY a line if ∠XOZ = 7x + 20° and ∠YOZ = 3x in figure.

Two supplementary angles are in the ratio 4 : 5. Find the angles.

 In figure, lines AB and CD intersect at O. If ∠AOD : ∠DOC = 4 : 5 then find ∠COB.

An angle is equal to five times of its complement. Find the measure of the angle.

In figure, lines I and m intersect each other at O. If x = 40°, then, find the values of y, z and w.

If OA, OB. OC and OD are the rays such that ∠AOB = ∠COD = 150°, ∠BOC = 30° and ∠AOD = 30°. Is it true that AOC and BOD are straight lines? Justify your answer.