Section 7.2 - Angle Properties Of Polygons

1)

What is the measure of angle x in this diagram?

60 degrees

80 degrees

120 degrees

240 degrees

The measure of angle x in the diagram is 60 degrees.

Explanation

The measure of angle x in the diagram is 60 degrees.

2)

Which shows an exterior angle

W

X

Y

Z

The correct answer is z because an exterior angle is formed when a side of a polygon is extended. In this case, z is the only angle that is outside the polygon and formed by extending one of its sides.

Explanation

The correct answer is z because an exterior angle is formed when a side of a polygon is extended. In this case, z is the only angle that is outside the polygon and formed by extending one of its sides.

3) What is the sum of the exterior angles in a regular 13-gon?

152.3 degrees

360 degrees

1980 degrees

3960 degrees

The sum of the exterior angles in any polygon, including a regular 13-gon, is always 360 degrees. This is a property of polygons, where the sum of the exterior angles is equal to a full rotation of 360 degrees. Therefore, the correct answer is 360 degrees.

Explanation

The sum of the exterior angles in any polygon, including a regular 13-gon, is always 360 degrees. This is a property of polygons, where the sum of the exterior angles is equal to a full rotation of 360 degrees. Therefore, the correct answer is 360 degrees.

4) Brian has been making octagonal wooden puzzles. He wants to make some hexagonal puzzles next. By how much does he need to increase or decrease the interior angle measure on his template to make the hexagonal puzzles?

Increase by 15 degrees

Decrease by 15 degrees

Increase by 35 degrees

Decrease by 35 degrees

To make hexagonal puzzles, Brian needs to decrease the interior angle measure on his template by 15 degrees. This is because an octagon has interior angles measuring 135 degrees, while a hexagon has interior angles measuring 120 degrees. Therefore, by decreasing the angle measure by 15 degrees, Brian will be able to create hexagonal puzzles.

Explanation

To make hexagonal puzzles, Brian needs to decrease the interior angle measure on his template by 15 degrees. This is because an octagon has interior angles measuring 135 degrees, while a hexagon has interior angles measuring 120 degrees. Therefore, by decreasing the angle measure by 15 degrees, Brian will be able to create hexagonal puzzles.

5)

What is the meansure of ÐACB is the diagram?

48 degrees

78 degrees

102 degrees

126 degrees

The measure of angle ACB in the diagram is 78 degrees.

Explanation

The measure of angle ACB in the diagram is 78 degrees.

6) What is the measure of an exterior angle of a regular polygon in which the sum of the interior angle measures is 5400 °

11.25 degrees

30 degrees

32 degrees

168.75 degrees

The measure of an exterior angle of a regular polygon is found by dividing 360 degrees by the number of sides in the polygon. In this case, the sum of the interior angle measures is given as 5400 degrees, which means each interior angle measures 5400/360 = 15 degrees. Since the exterior angle is supplementary to the interior angle, it must measure 180 - 15 = 165 degrees. However, none of the answer choices match this value, so the correct answer is not available.

Explanation

The measure of an exterior angle of a regular polygon is found by dividing 360 degrees by the number of sides in the polygon. In this case, the sum of the interior angle measures is given as 5400 degrees, which means each interior angle measures 5400/360 = 15 degrees. Since the exterior angle is supplementary to the interior angle, it must measure 180 - 15 = 165 degrees. However, none of the answer choices match this value, so the correct answer is not available.

7) In triangle LMN, the measure of ÐM is 4° more than twice the measure of Ð L. The measure of Ð N is 27° less than half the measure of Ð L. What is the measure of Ð N?

2 degrees

13.6 degrees

29 degrees

56 degrees

The measure of angle N is 27 degrees less than half the measure of angle L. Since the measure of angle L is not given, we cannot determine the exact measure of angle N. Therefore, we cannot confirm that the given answer of 2 degrees is correct.

Explanation

The measure of angle N is 27 degrees less than half the measure of angle L. Since the measure of angle L is not given, we cannot determine the exact measure of angle N. Therefore, we cannot confirm that the given answer of 2 degrees is correct.

8)

Home plate on a baseball diamond has 3 right angles. What is the sum of the measure of Ðx and Ðy

45 degrees

90 degrees

135 degrees

270 degrees

Home plate on a baseball diamond is a square shape, with each corner forming a right angle. Since it is mentioned that there are 3 right angles, it means that there is only one angle that is not a right angle. Therefore, the sum of the measure of Ðx and Ðy must be 90 degrees, as the only way to have 3 right angles in a square is if the remaining angle is also 90 degrees.

Explanation

Home plate on a baseball diamond is a square shape, with each corner forming a right angle. Since it is mentioned that there are 3 right angles, it means that there is only one angle that is not a right angle. Therefore, the sum of the measure of Ðx and Ðy must be 90 degrees, as the only way to have 3 right angles in a square is if the remaining angle is also 90 degrees.