Question

The line \(L_1\) is parallel to \(L_2\) and line \(L_3\) is parallel to \(L_4\). In the figure, the relation between \(a^\circ\) and \(b^\circ\) is

• A. Equal
• B. Complementary
• C. Supplementary
• D. \(a^\circ+b^\circ=150^\circ\)

Hint:

In parallel line problems, first identify equal corresponding/alternate angles, then check whether the required angles form a straight line.

Answer 1

The Correct Option is C

Since: \[ L_1 \parallel L_2 \] and \[ L_3 \parallel L_4 \] angles formed between these parallel pairs follow corresponding and alternate angle properties. Angle \(b^\circ\) on \(L_1\) with transversal \(L_3\) is equal to the corresponding angle made by \(L_4\) with \(L_2\). Now in the figure, \(a^\circ\) and that corresponding angle lie on a straight line. So: \[ a+b=180^\circ \] Hence, they are: \[ \boxed{\text{Supplementary}} \]