unit 3 - angles and parallels - test #3 quizlet

If mz2 = 137 and mz P= 22, what is mz 0?

115 Solution Key Since the measurement of angle 2 = 137, the measurement of angle 1 = 43. Therefore the measurement of angle O = 180 - (43 + 22) 180 - 65= 0 115 = 0

Approximately how many degrees are in the measure of an interior angle of a regular eight sided polygon?

135 Solution Key (n - 2)180 = (8 - 2)180 = 180(6) = 1080 1080/ 8= 135

In a right triangle, the acute angles measure x+15 and 2x degrees. What is the measure of the larger acute angle of the triangle?

50 Solution Key 90 + x + 15 + 2x = 180 3x + 105 = 180 3x = 75 x= 25 2(25) = 50

Find mz3 if m25 = 38 and m26 = 62.

80 Solution Key. Considering I and m are parallel, angle 7 and angle 3 are equal, since they are alternate angles of a transversal cutting two parallel lines. The measurement of angle 7= 180 - (38 + 62) Angle 7- 180 - 100 Angle 7= 80 Therefore; angle 3 = 80

The sum of the interior angles of an n-gon is 90° (n - 2).

False

The sum of the interior angles of a quadrilateral equals 340°.

False Solution Key The sum of the interior angles of a quadrilateral equals 340°. This is FALSE

The sum of the exterior angles of a pentagon equals 300°.

False Solution Key. The sum of the exterior angles of a pentagon equals 300° The exterior angles of every polygon sum to 360°, so this is FALSE.

An exterior angle of a triangle equals 180 minus the adjacent interior angle.

True

The sum of the interior angles of a triangle is 180°.

True Solution Key The sum of the interior angles of a triangle is 180°. The interior angles of a triangle sum to 180°, so this is TRUE.

Determine if the statement is always, sometimes or never true. A quadrilateral is a polygon.

always

Determine if the statement is always, sometimes or never true. An equilateral triangle is a regular polygon.

always Solution Key Always. A regular polygon has all equal sides. An equilateral has all equal sides.

One angle of a triangle is obtuse. The sum of the measures of the other angles must be:

less than 90 degrees Solution Key Less than 90 degrees. If one angle is obtuse, it measures more than 90 degrees. Thus the other two's sum must measure less than 90 degrees in order for all three angles to sum to 180 degrees.

Determine if the statement is always, sometimes or never true. There are 300 degrees in the sum of the interior angles of a polygon.

never Solution Key. Never. 300 is not a multiple of 180.

Determine if the statement is always, sometimes or never true. An exterior angle of a triangle is 180 degrees.

never Solution Key Never. This would mean that the interior angle is 0. This would not be a triangle.

Determine if the statement is always, sometimes, or never true. A scalene triangle is obtuse.

sometimes Solution Key Sometimes. There are other times in which all three legs are of different measures. This is dependent of the measurement of the other two angles.

Determine if the statement is always, sometimes or never true. Each of the interior angles in a polygon are equal in measure.

sometimes Solution Key Sometimes. This happens in the case of regular polygons.

Determine if the statement is always, sometimes or never true. The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.

sometimes Solution Key Sometimes. This happens in the case of squares and rectangles.

A triangle can have one right angle.

© True