In Fig. 102, AB || CD || EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is
(a) 35
(b) 50
(c) 30
(d) 40

Open in App

Solution

Since, AB || EG
∴ ∠ABG + ∠EGB = 180^∘ (Angles on the same side of a transversal line are supplementary)
⇒ 110^∘ + ∠EGB = 180^∘
⇒ ∠EGB = 70^∘
Again, CD || GF
∴ ∠DCG + ∠FGC = 180^∘ (Angles on the same side of a transversal line are supplementary)
⇒ 100^∘ + ∠FGC = 180^∘
⇒ ∠FGC = 80^∘
Now, ∠EGB + ∠BGC +∠FGC = 180^∘
⇒ 70^∘ + x^∘ + 80^∘= 180^∘
⇒ 150^∘+ x^∘ = 180^∘
⇒ x^∘ = 30^∘
⇒ x = 30
Hence, the correct answer is option (c).

Suggest Corrections

Similar questions

Mark (✓) against the correct answer
In the given figure, AB || CD || EF, ∠ABG = 110°, ∠GCD = 100° and ∠BGC = x°.
Then x = ?

(a) 35
(b) 50
(c) 30
(d) 40

In figure, if $A B ∥ C D$ . The value of $x$ is
(a) $122$
(b) $238$
(c) $58$
(d) $119$

Q. In Fig. 91, AOB is a straight line and 4x = 5y. The value of x is
(a) 100
(b) 105
(c) 110
(d) 115

In the given fig., angle OBC = 30^o, then value of x is:

Q. For a real number x, [x] denotes the integral part of x. The value of

[\frac{1}{2}] + [\frac{1}{2} + \frac{1}{100}] + [\frac{1}{2} + \frac{1}{100}] + . . . + [\frac{1}{2} + \frac{99}{100}]

Join BYJU'S Learning Program

In Fig. 102, AB || CD || EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is (a) 35 (b) 50 (c) 30 (d) 40

In Fig. 102, AB || CD || EF, ∠ABG = 110°, ∠GCO = 100° and ∠BGC = x°. The value of x is
(a) 35
(b) 50
(c) 30
(d) 40