Question

in the figure ab is parallel to cd. find the values of ∠1, ∠2 and ∠3

Explanation:

Step1: Use linear - pair property

$\angle1$ and the $100^{\circ}$ angle form a linear - pair. A linear - pair of angles is supplementary, i.e., their sum is $180^{\circ}$. So, $\angle1=180^{\circ}- 100^{\circ}=80^{\circ}$.

Step2: Use corresponding - angles property

Since $AB\parallel CD$, $\angle1$ and $\angle3$ are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are equal. So, $\angle3 = \angle1=80^{\circ}$.

Step3: Use linear - pair property again

$\angle2$ and $\angle3$ form a linear - pair. So, $\angle2=180^{\circ}-\angle3$. Substituting $\angle3 = 80^{\circ}$, we get $\angle2 = 100^{\circ}$.

Answer:

$\angle1 = 80^{\circ}$, $\angle2 = 100^{\circ}$, $\angle3 = 80^{\circ}$