MATHS Fill In The Blanks[1 Marks ]

If a transversal intersects a pair of lines in such a way that the sum of interior angles on the seine side of transversal is 180'. then the lines are parallel.

If the sum of two adjacent angles is 180°, then the Uncommon arms of the two angles are opposite rays.

The complement of an acute angle is an acute angle.
Explanation:
As the sum of the complementary angles is 90°.
Let one of the angle measures x°.
Then, other angle becomes(90 - x)°, which is clearly an acute angle.

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are supplementary.

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

If a transversal intersects a pair of lines in such a way that a pair of alternate angles we equal. then the lines are parallel.

If one angle of a linear pair is acute, then its other angle will be Obtuse.

If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal.

The supplement of an acute angle is an obtuse angle.
Explanation:
As the sum of the supplementary angles is180°.
Let one of the angle measure x°, such that x < 90.
Let the other angle measures y°.
As the angles are supplementary there sum is 180°.
x + y = 180° ...(1)
x < 90° ...(2)
Now subtracting (1) from (2)
-y < -90°
y > 90°
Then, other angle y is clearly an obtuse angle.
Illustration:
Let the given acute angle be 30°
Then, the other angle becomes
(180 - 30)° = 150°
This is clearly an obtuse angle.

We have to find the supplement of a right angle.
We know that a right angle is equal to 90°.
Let the required angle be x°.
Since the two angles are supplementary, therefore their sum must be equal to 180°.
Thus, the require angle becomes
x = (180 - 90)°
x = 90°

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

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