Question

$\mathbf{\angle }\mathbf{5}$and$\mathbf{\angle }\mathbf{3}$ are? angles.

Short answer

$\angle 5$and$\angle 3$ are alternate interior angles.

Step-by-step solution

Step 1. Highlight ∠5 and src="data:image/svg+xml;base64,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" role="math" localid="1649999246557" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/c8391f47-08d1-44e0-a272-03995933c315.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220415%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220415T050944Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=8455393d0147765f33570e734b828c16865a4dd650eba961e69c2b822a466d9b" ∠3 in the given diagram.

Step 2. Apply the definition of alternate interior angles.

When two parallel lines are intersected by a transversal then the angles formed on the inner side of the parallel lines but, on the opposite sides of the transversal are alternate interior angles.

Step 3. Description of step.

From the given figure it can be observed that$r\parallel s$and$t$ is transversal then by the definition of alternate interior angles,$\angle 5$and$\angle 3$ are alternate interior angles.

Therefore,$\angle 5$ and$\angle 3$ are alternate interior angles.