Question

Count and name all the angles in these figures: -
(i)

(ii)

Answer 1

Hint: To name the angle observe the three vertices or two sides that form the angle. The vertex at which the angle is being formed must lie in the middle of the name. Now, first consider the figures of the triangle ABC and the quadrilateral ABCD one by one and use the fact that the number of angles in a closed 2 – D figure is equal to the number of sides in the same 2 – D figure and name each angle.

Complete step by step answer:
Here we have been provided with two figures one of triangle ABC and the other of the quadrilateral ABCD. We have been asked to count and name all the angles of these figures. Let us first understand the term angle.
In mathematics, an angle is formed when two rays meet at a particular point. A diagram is shown below for better clarification.

As we can see that the three points A, O and B form an angle at O, so the naming of this angle is done in such a way that the letter O will always remain in the middle. The name of the angle can be given as $\angle AOB$ or $\angle BOA$, both are the same. It can simply be named as angle O also. Let us come to the question.
(i)

Here we have the triangle ABC. We know that a triangle has three sides and in a 2 – D shape the number of sides is equal to the number of angles. So the number of angles in the triangle ABC is 3. According to the convention of naming these angles we have the name of these angles as $\angle ABC$, $\angle BCA$ and $\angle CAB$.

(ii)

Here we have the quadrilateral ABCD. We know that a quadrilateral has four sides, so the number of angles in the quadrilateral ABCB is 4. According to the convention of naming these angles we have the name of these angles as $\angle ABC$, $\angle BCD$, $\angle CDA$ and $\angle DAB$.
Hence, the triangle ABC has 3 angles whose names are $\angle ABC$, $\angle BCA$, $\angle CAB$ and quadrilateral has 4 angles whose names are $\angle ABC$, $\angle BCD$, $\angle CDA$, $\angle DAB$.

Note: Note that these were simple triangles, quadrilaterals and the angles were not divided by any line so you can name them simply as angle A, B, C in the triangle and angle A, B, C and D in the quadrilateral. In some cases when a line divides the angle then you have to name the angle as per the question asked because the angle gets divided into two parts and it may be asked to write the name of only one part. In such cases we often use the convention of naming as used in the above solution.