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Question
Two parallel lines l and m cut by a transversal t. If the interior angles of the same side of t be (2x − 8)° and (3x − 7)°, find the measure of each of these angles.
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Solution
Given: l∥m and t is a transversal. Let: ∠1 =(2x-8)° and ∠2 = (3x-7)°
We know that the consecutive interior angles are supplementary
.∴ ∠1 +∠2 =180°
or (2x-8) + (3x-7) =180
or 5x -15 = 180
or 5x = 195
or x = 39
So, ∠1 = (2x-8) = (2×39-8) =78-8=70° and ∠2 =(3x-7) = (3×39-7)=117-7 = 110°
Given: l∥m and t is a transversal. Let: ∠1 =(2x-8)° and ∠2 = (3x-7)°
We know that the consecutive interior angles are supplementary
.∴ ∠1 +∠2 =180°
or (2x-8) + (3x-7) =180
or 5x -15 = 180
or 5x = 195
or x = 39
So, ∠1 = (2x-8) = (2×39-8) =78-8=70° and ∠2 =(3x-7) = (3×39-7)=117-7 = 110°
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