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One of the same side interior angles of two pararrel lines is 20 degrees less than the other same side interior angle. Find the measures of the two angles

User Betamoo
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The larger interior angle on the same side of the transversal measures 108 degrees.

The two interior angles are on the same side of the transversal and the lines are parallel, they are supplementary angles (sum to 180 degrees). Let x be the measure of the smaller angle. Then the larger angle is 3x/2. Since they are supplementary, we have:

x + 3x/2 = 180

Combining like terms:

5x/2 = 180

Multiplying both sides by 2/5:

x = 72

Therefore, the smaller angle measures 72 degrees and the larger angle measures 3*72/2 = 108 degrees.

Question:
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:

User Omar Abdirahman
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