Angles whose measures are 115° and 65° are a pair of complementary angles.
We have 115°+65°=180° Hence, 115° and 65° are a pair of supplementary angles.
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°
