In the adjoining figure, identify $(i)$ the pairs of corresponding angles. $(ii)$ the pairs of alternate interior angles. $(iii)$ the pairs of interior angles on the same side of the transversal. $(iv)$ the vertically opposite angles."

To do:

We have to identify

(i) the pairs of corresponding angles.

(ii) the pairs of alternate interior angles.

(iii) the pairs of interior angles on the same side of the transversal.

(iv the vertically opposite angles.

Solution:

(i) The pairs of corresponding angles are $\angle 1$ and $\angle 5,\ \angle 2$ and $\angle 6,\ \angle 4$ and $\angle 8,\ \angle 3$ and $\angle 7$

(ii) The pairs of alternate interior angles are $\angle 2$ and $\angle 8$; $\angle3$ and $\angle 5$

(iii) The pairs of interior angles on the same side of the transversal are $\angle 2$ and $\angle 5,\ \angle 3$ and $\angle 8$.

(iv) $\angle 1$ and $\angle 3$; $\angle 2$ and $\angle 4$; $\angle 6$ and $\angle 8$; $\angle 5$ and $\angle 7$ are the vertically opposite angles.

Related Articles Indicate which pairs of angles are:$(i)$ Vertically opposite angles. $(ii)$ Linear pairs."
In the adjoining figure, name the following pairs of angles.(i) Obtuse vertically opposite angles(ii) Adjacent complementary angles(iii) Equal supplementary angles(iv) Unequal supplementary angles(v) Adjacent angles that do not form a linear"\n
In the adjoining figure, name the following pairs of angles.$(i)$ Obtuse vertically opposite angles$(ii)$ Adjacent complementary angles$(iii)$ Equal supplementary angles$(iv)$ Unequal supplementary angles$(v)$ Adjacent angles that do not form a linear pair"
In the figure, write all pairs of adjacent angles and all the linear pairs."\n
What is the difference between supplementary angles and complementary angles and also linear pairs of angles?
Explain the concept of interior and exterior angles.
Draw a rough sketch of a quadrilateral KLMN. State,(a) two pairs of opposite sides,(b) two pairs of opposite angles,(c) two pairs of adjacent sides,(d) two pairs of adjacent angles.
One of the exterior angles of a triangle is 100°. The interior opposite angle is 75°. Find the measure of all the angles of the triangle?
Give the proof of Theorem of vertically opposite angles.
Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.
Fill in the blanks in each of the following to make the statement true:If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ________________
How many pairs of adjacent angles, in all, can you name in the figure?"\n
Fill in the blanks:$(i)$ If two angles are complementary, then the sum of their measures is _______.$(ii)$ If two angles are supplementary, then the sum of their measures is ______.$(iii)$ Two angles forming a linear pair are _______________.$(iv)$ If two adjacent angles are supplementary, they form a ___________.$(v)$ If two lines intersect at a point, then the vertically opposite angles are always _____________.$(vi)$ If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.
Two parallel lines $l$ and $m$ cut by a transversal $t$. If the interior angles of the same side of $t$ be $(2 x-8)°$ and $(3 x-7)°$, find the measure of each of these angles.
Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.
Kickstart Your Career
Get certified by completing the course

Get Started