what is the justification of 120 degree angle?
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Solution:-
Steps for construction of 120° angle :
1) Draw a ray XY
2) Draw an arc with X as center and any convenient radius intersecting xy at P.
3) Taking P as center and same radius as taken before, draw an arc intersecting previous arc at Q.
4) From Q, draw an arc of the same radius cutting the arc taken in the beginning of the construction at R.
5) Draw a ray XM passing through R.
Thus, MXY = 120°
Justification :
Arcs at point Q and R are drawn taking the same radius. Hence we can say that arcs PQ and QR are equal. Hence they subtend equal angles at the center X. Now, if we join the points X and Q then Δ XQP will be an equilateral triangle (as XP = PQ = XQ). Hence QP subtends an angle of 60° at the center.
So, angle subtended by the arc PR = angle subtended by arc PQ + angle subtended by arc QR
= 60° + 60° = 120°
Steps for construction of 120° angle :
1) Draw a ray XY
2) Draw an arc with X as center and any convenient radius intersecting xy at P.
3) Taking P as center and same radius as taken before, draw an arc intersecting previous arc at Q.
4) From Q, draw an arc of the same radius cutting the arc taken in the beginning of the construction at R.
5) Draw a ray XM passing through R.
Thus, MXY = 120°
Justification :
Arcs at point Q and R are drawn taking the same radius. Hence we can say that arcs PQ and QR are equal. Hence they subtend equal angles at the center X. Now, if we join the points X and Q then Δ XQP will be an equilateral triangle (as XP = PQ = XQ). Hence QP subtends an angle of 60° at the center.
So, angle subtended by the arc PR = angle subtended by arc PQ + angle subtended by arc QR
= 60° + 60° = 120°
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