Question

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

Answer 1

$$\begin{gathered} \left(c\right)30 \\ \begin{array}{l}\text{Here,}\angle \text{DCG}+\angle \text{CGF}={180}^0(\mathrm{angles}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{transversal}\mathrm{line}\mathrm{are}\mathrm{supplementary})\\ =>\angle \text{CGF}={180}^0-100°=80°\\ \angle \text{ABG}=\angle \text{BGF}={110}^0\left[\text{alternate angles}\right]\\ x^0+\angle \text{CGF}={110}^0\\ =>x^0={110}^0-{80}^0\\ =>x^0={30}^0\end{array} \\ \therefore x=30 \end{gathered}$$