NCERT Solutions for Class 7th Maths Chapter 6 Repeating Units and Repeating Angles — In-text Questions
Book page 145 Updated on2026-09-19
Q1.
Construct the following figure.
Fig. 6.6, page 145.
Answer
The whole figure is one unit, repeated. The unit is a fan shape: two straight arms of equal length meeting at a point, closed off by an arc. Copies are laid down alternately point-up and point-down.
Draw the unit once: mark a vertex V, draw two arms VA and VB of equal length with some angle between them, and join A to B with an arc of centre V.
To repeat it, you must copy both the arm length and the angle. The arm length is easy — carry it with the compass.
Copy the angle by the arc-and-chord method: draw an arc from V cutting the arms at A and B; draw the same arc at the new vertex; then transfer the chord AB with the compass.
Place the copies alternately: point down, point up, point down, … so that neighbouring units share an endpoint.
Why it happens: two fans are exact copies only if their arms match and the angle between the arms matches. Equal arms alone are not enough — a wide fan and a narrow fan can have the same arm length. That is why the chapter now needs a way to copy an angle.
Tip: mark the shared endpoints on a straight line first. Then every unit starts and ends where its neighbours do, and the wave stays level.
Q2.
Draw an angle. Create a copy of this angle using only a ruler and compass.
Answer
Turn the angle into a triangle, then rebuild the same triangle somewhere else. SSS congruence carries the angle across.
Let the given angle be at A. Draw a ray from the new point X.
With centre A and any radius, draw an arc cutting the two arms of the angle at B and C. Now ΔABC is isosceles with AB = AC.
With the same radius and centre X, draw an arc cutting the new ray at Z.
Open the compass to the length BC. With centre Z, cut the new arc at Y, so YZ = BC.
Join X to Y. Then ∠YXZ = ∠BAC.
AB = XZ (same radius) — call it r
AC = XY (same radius) — also r
BC = YZ (chord transferred with the compass)
⇒ ΔABC ≅ ΔXYZ by SSS
⇒ ∠A = ∠X
Why it happens: a compass cannot measure an angle, but it can measure a length. So we convert the angle into a length — the chord BC across the arc. With the two radii fixed, the chord decides the angle completely: a wider angle gives a longer chord. Copy the chord and the angle comes with it.
Check it yourself: after copying, place the arc-and-chord of the copy over the original by tracing on thin paper. They should fall exactly on each other.