Given that: AB || CD, m∠CSK = (7x + 10)°, m∠ARL = (8x + 5)°. Find the m∠KSD in degrees.

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4. Given that: AB || CD, m∠CSK = (7x + 10)°, m∠ARL = (8x + 5)°. Find the m∠KSD in degrees.

SnapAndSolve AI · Accepted Answer

Solution: Since AB || CD and RS is a transversal, ∠CSK and ∠ARL are alternate interior angles, so they are equal. Set the expressions equal: 7x + 10 = 8x + 5. Solve for x: 7x + 10 = 8x + 5 implies 10 - 5 = 8x - 7x, which simplifies to 5 = x. Substitute x = 5 into m∠CSK: m∠CSK = 7(5) + 10 = 35 + 10 = 45°. Since ∠KSD is vertically opposite to ∠CSK, m∠KSD = 45°. The m∠KSD is 45 degrees.

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Given that: AB || CD, m∠CSK = (7x + 10)°, m∠ARL = (8x + 5)°. Find the m∠KSD in degrees.

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