NCERT Solutions Ganita Prakash Chapter 2 Figure it Out — Drawing Angles
Book page 49 & 50 Updated on2026-09-05
Q1.
In Fig. 2.23, list all the angles possible. Did you find them all? Now, guess the measures of all the angles. Then, measure the angles with a protractor. Record all your numbers in a table. See how close your guesses are to the actual measures.
Answer
Fig. 2.23 is made of two parallel lines — one through A, P, R, B and one through C, D, L, S — cut by three transversals: AC, PL and RS. Work vertex by vertex so that no angle is left out.
Fig. 2.23 — two parallel lines cut by three transversals, with the measures read off the printed figure.
All the angles you can list (each vertex carries four angles, of which two are marked below):
Vertex
Angle
Measured value
Type
A
∠CAP (= ∠CAB)
107°
obtuse
∠CA(left part of the line)
73°
acute
C
∠ACD (= ∠ACL, ∠ACS)
73°
acute
∠AC(left part of the line)
107°
obtuse
P
∠APL
82°
acute
∠RPL (= ∠BPL)
98°
obtuse
L
∠SLP
82°
acute
∠DLP (= ∠CLP)
98°
obtuse
R
∠PRS (= ∠ARS)
102°
obtuse
∠BRS
78°
acute
S
∠LSR (= ∠CSR, ∠DSR)
78°
acute
∠RS(right part of the line)
102°
obtuse
Now copy this table into your notebook with an extra column for your guess, and see how close you were:
Angle
My guess
Measured value
Difference
∠CAP
…
107°
…
∠ACD
…
73°
…
∠APL
…
82°
…
∠DLP
…
98°
…
∠PRS
…
102°
…
∠BRS
…
78°
…
Two useful checks: the two angles at any one crossing add up to 180° (107 + 73, 82 + 98, 102 + 78), and because the two lines are parallel, the angle a transversal makes at the top line is repeated at the bottom line. That is why ∠CAP = 107° goes with ∠ACD = 73°, and ∠APL = ∠SLP = 82°.
Tip for listing angles: pick one corner point, note every ray coming out of it, and then take those rays two at a time. Move to the next corner only when the first is finished — that way you will not miss any angle or count one twice.
Q2.
Use a protractor to draw angles having the following degree measures: a. 110° b. 40° c. 75° d. 112° e. 134°
Answer
Follow the same four steps for each angle — here they are for 110°:
Draw a ray with a ruler; call it OB. This is the base arm.
Place the centre of the protractor exactly on O, with OB along the 0 line.
Starting from 0, count up the scale to 110 and mark a dot there. Call it A.
Remove the protractor and join O to A. Then ∠AOB = 110°.
Angle to draw
Mark the point at
Type
a. 110°
the 110 mark
obtuse
b. 40°
the 40 mark
acute
c. 75°
the 75 mark
acute
d. 112°
between 110 and 115, on the 112 mark
obtuse
e. 134°
between 130 and 135, on the 134 mark
obtuse
Tip: after drawing, measure the angle once again to check. And use the scale that starts from 0 on your base arm — the other scale would give 70° instead of 110°.
Q3.
Draw an angle whose degree measure is the same as the angle given below. Also, write down the steps you followed to draw the angle.
Answer
Step 1 — measure the given angle. Put the centre of the protractor on the vertex I, place the arm IJ on the 0 line and read where IH crosses the scale. Suppose the reading is 65°.
Step 2 — draw your own angle of the same measure.
Draw a ray QR with a ruler.
Place the centre of the protractor on Q, with QR along the 0 line.
Count from 0 up to the measured value (65) and mark a point P.
Join Q to P. Now ∠PQR = ∠HIJ.
The given angle ∠HIJ measures 65°, and the angle ∠PQR drawn beside it has the same measure — even though its arms are longer.
Step 3 — check. Trace your angle on tracing paper and place it on the given angle, vertex on vertex and arm on arm. The other two arms should fall exactly on each other.
Tip: the two angles need not have arms of the same length — only the turn between the arms has to match.