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If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the greater of the two angles is:
108°
54°
136°
120°
108°
Let the angles be 2x and 3x. Since their sum is 180° for parallel lines, 2x+3x=5x=180°⟹x=36°. The greater angle is 3x=3×36°=108°.
Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3.
Sum of interior angles on the same side of transversal=180°
Let the angles be 2x and 3x. Since their sum is 180° for parallel lines, 2x+3x=5x=180°⟹x=36°. The greater angle is 3x=3×36°=108°.
Confusing interior angles on the same side of the transversal (which add up to 180°) with alternate interior angles (which are equal).
Step 1: Understand parallel lines property
When a transversal intersects two parallel lines, the interior angles on the same side of the transversal are supplementary, meaning their sum is 180°.
∠1+∠2=180°
Step 2: Assign variables based on the ratio
Given that the ratio of the two interior angles is 2:3, we can let the two angles be 2x and 3x.
Angle1=2x,Angle2=3x
Step 3: Set up and solve the equation
Sum the two angles and equate them to 180°:
2x+3x=180°⟹5x=180°⟹x=36°
Step 4: Find the greater angle
Substitute x=36° into the expression for the greater angle (3x):
Greater Angle=3×36°=108°
A is correct because the two interior angles are 2x and 3x which sum to 180°, giving 5x=180°⟹x=36°, and the greater angle is 3×36°=108°.
This fundamental angle property is widely used in coordinate geometry and polygon exterior/interior angle sums.
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