The interior angles which appear opposite sides of transversal of nonparallel lines are called the alternate interior angles formed by nonparallel lines and their transversal line.

When two nonparallel lines are intersected by their transversal, four interior angles are formed geometrically but every two of them are appeared opposite sides at the intersection of the non-parallel lines by their transversal line. Hence, two pairs of alternate interior angles are formed by the intersection.

When two nonparallel lines ($\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$) are intersected by their transversal line $\overleftrightarrow{XY}$, four interior angles $\angle YPA$, $\angle YPB$, $\angle XQC$ and $\angle XQD$ are formed geometrically.

The following two pairs of interior angles are alternate interior angles.

$1. \,\,\,\,\,\,$ $\angle YPA$ and $\angle XQD$

$2. \,\,\,\,\,\,$ $\angle YPB$ and $\angle XQC$

Each pair of alternate interior angles are not equal. It is mainly due to the involvement of nonparallel lines in the intersection with their transversal line.

$1. \,\,\,\,\,\,$ $\angle YPA \,\ne\, \angle XQD$

$2. \,\,\,\,\,\,$ $\angle YPB \,\ne\, \angle XQC$

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.