Question

Given that line $p$ is parallel to line $q$the value of $x$ in the figure can be found out by

• A. Alternate-Interior Angle Theorem
• B. Corresponding Angle Theorem
• C. Co-Interior Angle Theorem
• D. None

Answer 1

Answer: (A), (B), (C)

Co-Interior Angle Theorem

The value of $x$ in the above figure can be found out by any of the three theorems like Alternate interior angle theorem, Corresponding angle theorem or co interior angle theorem.

Alternate interior angle theorem:

$\angle 1={62}^o\angle 1+x^o={180}^o\left(\text{linear pair}\right){62}^o+x^o={180}^o{x}^o={118}^o$

Co-Interior Angle Theorem:

$\angle 2+{62}^o={180}^o\angle 2={180}^o-{62}^o={118}^o\angle 2=x^o\left(\text{Vertically opposite angle}\right)x^o={118}^o$

Corresponding Angle Theorem:

$\angle 3={62}^o\angle 3+x^o={180}^o\left(\text{Linear pair}\right){62}^o+x^o={180}^o{x}^o={180}^o-{62}^o={118}^o$

Hence, options $\left(a\right)$ $\left(b\right)$ and $\left(c\right)$ are correct.