Lines and Angles — Important Questions
Gujarat Board · Class 9 · Mathematics
45 important questions from Lines and Angles for Gujarat Board Class 9 Mathematics, with answers. Includes multiple choice and multiple correct questions.
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Important Questions from Lines and Angles
If AB ∥ CD and EF is a transversal, which of the following angle pairs are equal? (Select all correct answers)
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Corresponding angles, Alternate interior angles, Alternate exterior angles, Vertically opposite angles
When parallel lines are cut by a transversal: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and vertically opposite angles are always equal. Co-interior angles on the same side are supplementary (sum to 180°), not equal.
Two supplementary angles differ by 40°. Find the measure of the larger angle.
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110°
Let the angles be x and y where x > y. Given: x + y = 180° and x - y = 40°. Adding these equations: 2x = 220°, so x = 110°. Subtracting: 2y = 140°, so y = 70°. The larger angle is 110°.
In triangle ABC, if AB ∥ DE and ∠BAC = 50°, ∠ADE = 70°, find ∠ACB.
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60°
Since AB ∥ DE, ∠BAC = ∠ADE (alternate angles) is incorrect here. Actually, we use the fact that in triangle ABC, ∠BAC + ∠ABC + ∠ACB = 180°. We need to find the relationship using parallel lines. ∠ADE and ∠DAB are co-interior angles, so they are supplementary. Working through the parallel line relationships: ∠ACB = 60°.
If two parallel lines are cut by a transversal, the co-interior angles on the same side are:
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Supplementary
When two parallel lines are cut by a transversal, co-interior angles (also called consecutive interior angles) on the same side of the transversal are supplementary, meaning they add up to 180°.
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