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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 20 Page 467

Compare the angles to a right angle.

∠ 1

Consider the given diagram. On the figure, the red marker indicates that the two lines are perpendicular. This means that ∠ 4, ∠ 7, and ∠ 9 are all right angles. m∠ 4=m∠ 7=m∠ 9=90 Let's shade two of the right triangles on the figure.

Now, to find which angle has the greatest measure, we will first estimate the measures of each angle.

Estimating m∠ 1

According to the Exterior Angle Theorem, the measure of an exterior angle is the sum of the measures of the two remote interior angles. Let's apply this to the first right triangle.

Notice that ∠ 1 is an exterior angle and ∠ 3 and ∠ 4 are the corresponding remote interior angles. m∠ 1=m∠ 3+ m∠ 4 Because ∠ 4 is a right angle, ∠ 1 is an obtuse angle.

Estimating m∠ 5 and m∠ 6

In the second right triangle, ∠ 7 is a right angle.

According to Corollary 4.2 to the Triangle Angle-Sum Theorem, the other two angles, ∠ 5 and ∠ 6, must be acute.

Conclusion

Since ∠ 1 is an obtuse angle, and ∠ 5 and ∠ 6 are acute angles, out of these three angles, ∠ 1 has the greatest measure.