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Consider parallelogram ABCD below.

Use the information given in the figure to find m/BAC, m/B, and x.

Consider parallelogram ABCD below. Use the information given in the figure to find-example-1

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Answer:

Since opposite angles in a parallelogram are congruent, we know that:

m∠DAB = m∠BCD = 67°

Since ∠BAC and ∠BCD are adjacent angles, we know that:

m∠BAC + m∠BCD = 180°

So we can solve for m∠BAC:

m∠BAC + 67° = 180°

m∠BAC = 113°

Since opposite angles in a parallelogram are congruent, we know that:

m∠BAD = m∠BC

So we can solve for m∠BC:

m∠BAD = 16

m∠BC = 16°

Finally, we can solve for x by using the fact that the interior angles of a quadrilateral sum to 360 degrees:

m∠DAB + m∠BAC + m∠BCD + m∠CDA = 360°

67° + 113° + m∠BCD + 90° = 360°

m∠BCD = 90°

So we can solve for x:

m∠4B - m∠BCD = 90° - 90° = 0

4x - 59° = 0

4x = 59°

x = 14.75°

Therefore, m/BAC = 113°, m/B = 16°, and x = 14.75°.

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