Question

How many right angles are there in the given figure?

A. $ 2 $
B. $ 4 $
C. $ 8 $
D. $ 16 $

Answer 1

Hint: In order to deal with this question we have to use the properties of angles such that the sum of all the angles on one side of a straight line is always $ 180 $ degrees and angles that are opposite to each other at the intersection point are known as vertically opposite angles , vertically opposite angles are always equal.

Complete step-by-step answer:
First let us labelling the given figure

Let us consider A point
Here at a point A there are four angles
And given that $ \angle PAQ{\text{ }} = {\text{ }}90^\circ $
As we know that angles that are opposite to each other at the intersection point are known as vertically opposite angles , vertically opposite angles are always equal.
So here \[\angle PAQ\] and \[\angle BAC\] are vertically opposite angles and both are always equal to each other
Therefore $ \angle PAQ = \angle {\text{BAC = }}{90^0} $
Now as we know that the sum of all the angles on one side of a straight line is always 180 degrees.

\[{\text{ }}\angle QAB\; + {\text{ }}\angle BAC{\text{ }} = {\text{ }}{180^0}\]
By substituting value of \[\angle BAC\] we get
\[{\text{ }}\angle QAB\; + {\text{ 9}}{{\text{0}}^0}{\text{ }} = {\text{ }}{180^0}\]
\[\angle QAB = {\text{ }}{90^0}\]
Again by definition of vertically opposite angles
\[\angle QAB\] and \[\angle PAC\] are vertically opposite angles and both are equal to each other.
Therefore \[\angle QAB{\text{ }} = {\text{ }}\angle PAC{\text{ }} = {\text{ }}{90^0}\]
Hence at a point A there are $ 4 $ right angles , similarly at each point B,C, and D there will $ 4 $ right angles
So the total right angles will be \[4{\text{ }} + {\text{ }}4{\text{ }} + {\text{ }}4{\text{ }} + {\text{ }}4{\text{ }} = {\text{ }}16\]
Hence the correct answer is option D.

Note: Right angle is known as the angle with $ {90^0} $. If two lines intersect a linear pair of angles is formed. Two angles are said to be linear, if two lines are intersecting form opposite angles. A straight angle measurement is $ {180^0} $. So a linear pair of angles will add up to $ {180^0} $ .