#### If two lines intersect each other, then the vertically opposite angles are equal.

If two lines intersect each other, then the vertically opposite angles are equal.

#### If two parallel lines are intersected by a transversal, then the corresponding angles are equal.

If two parallel lines are intersected by a transversal, then the corresponding angles are equal.

#### Two lines perpendicular to the same line are perpendicular to each other.

Two lines perpendicular to the same line are parallel to each other.

#### If a ray stands on a line, then the sum of the adjacent angles so formed is ____

If a ray stands on a line, then the sum of the adjacent angles so formed is 180°.

#### If an angle is 20° less than its complement, then the measure of the angle is ____.

Let the measure of the required angle be x. Then, the measure of its complement is (90 − x) ° (90 – x) – x = 20° ⇒ 90 – 2x = 20 ⇒ - 2x = 20 – 90 ⇒ - 2x = - 70 ⇒ x = 35°

#### The supplement of an angle is one-third of itself, then the angle is ____.

The measure of its supplement is (180 – x)° 180 – x = (1 /3) x ⇒ 3(180 – x) = x ⇒ 4x = 540 ⇒ x = 135° Hence, the measure of required angle is 135°.

#### If an angle is equal to four times of its complement, then its measure is ____.

Let the measure of the given angle be x. x = (90 – x) ⇒ x = 360 − 4x ⇒ 5x = 360 ⇒ 5x = 360 / 5 ⇒ x = 72° Hence, the measure of the given angle is 72°.

#### Any point on the perpendicular bisector of a line segment is equidistant from its end points.

Any point on the perpendicular bisector of a line segment is equidistant from its end points.

#### An angle is equal to 8 times of its complement, then its measure is ____.

Let the measure of the given angle be x. The measure of its complement is (90 – x)° x = 8(90 - x) ⇒ x = 720 – 8x ⇒ 9x = 720 ⇒ x = 80° Hence, the required angle is 80°