Question

In the figure given below $L_1 || L_2$ then x = __________.

• A. 30
• B. 45
• C. 60
• D. Cannot be determined

Answer 1

Answer: (B)

45

Answer 2

Based on the information provided and the geometric relationships described:
1. Let angle $\angle HBG = 2y$ and $\angle BAF = 2y$ (corresponding angles are equal).
2. $\angle FAC = y$ and $\angle CAB = 180^\circ - 2y$ (sum of angles in a triangle).
3. $\angle ABG = y$ and $\angle ABC = 90^\circ - y$.
Given that $\angle ACB$ (which is denoted as $x$) is not explicitly stated but inferred to be equal to $\angle ABC$ due to geometric properties:
$\angle ACB = \angle ABC = 90^\circ - y$.
Since $2x = 90^\circ$ (from the equation $\angle ABC = 90^\circ - y$), solving for $x$:
$2x = 90^\circ$
$x = \frac{90^\circ}{2}$
$x = 45^\circ$
Therefore, $x = 45$ degrees, which corresponds to answer option B 45.