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If one angle is 24∘24 ∘ less than twice the smaller angle in a parallelogram, then the smaller angle is ________

Question

If one angle is 24° less than twice the smaller angle in a parallelogram, then the smaller angle is ________

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Solution

In a parallelogram, the sum of two adjacent angles is 180 degrees. Let's denote the smaller angle as x. According to the problem, the larger angle is 2x - 24.

So, we can set up the equation:

x + 2x - 24 = 180

Solving this equation will give us the value of x, which is the smaller angle.

First, combine like terms:

3x - 24 = 180

Then, add 24 to both sides of the equation:

3x = 204

Finally, divide both sides by 3 to solve for x:

x = 68

So, the smaller angle is 68 degrees.

This problem has been solved

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