Internal one-sided angles, formed at the intersection of two parallel straight lines of the third

| July 14, 2021 | education

Internal one-sided angles, formed at the intersection of two parallel straight lines of the third straight line, are related as 2: 3. What are these angles equal to?

Let’s denote the value of the angle ABC through 2 * X0, then, by condition, the angle BAD = 3 * X0.

The angles DAB and KAВ are adjacent angles, the sum of which is 180, then the angle KAВ = (180 – 3 * X) 0.

By condition, the straight line CE is parallel to the straight line DK, then the angle KAВ is equal to the angle ABC as the criss-crossing angles at the intersection of parallel straight lines DK and CE of the secant AB. Then the angle KAВ = ABC = 2 * X0.

180 = (2 * X + 3 * X) = 5 * X.

X = 180/5 = 36.

Then the angle ABC = 2 * 36 = 72, the angle DAB = 3 * 36 = 108.

Answer: The inner one-sided corners are 72 and 108.



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