Question

Draw an angle of 110° with the help of a protector and bisect it measure each of these angles, Justify your answer ​

Answer 1

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$\huge\underline\bold\orange{Question}$

• Draw an angle of 110° with the help of a protector and bisect it measure each of these angles, Justify your answer

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$\huge\underline\bold\orange{Solution}$

${\blue{\sf\underline{Steps\:of\: construction}}}$

$\purple{(i)}$ Draw ∠AOB = 110° with the help of a protector.

$\purple{(ii)}$With O as centre and a convenient radius, draw an arc cutting OA at P and OB at Q.

$\purple{(iii)}$ With P as a centre and a convenient radius, draw an arc.

$\purple{(iv)}$With Q as centre and with the same radius, draw another arc, cutting the previous arc at a point C.

$\purple{(v)}$ Join OC and produce it beyond C.

Then, OC is the required bisector of ∠AOB.

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${\blue{\sf\underline{Verification}}}$

On measuring ∠AOC and ∠BOC, you will find that

∠AOC = 55° and ∠BOC = 55°

Thus, ∠AOC = ∠BOC = 55° and therefore, OC is the bisector of ∠AOB.

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${\blue{\sf\underline{Justification}}}$

Join CP and CQ.

In ∆OPC and ∆OQC, we have

OP = OQ (radii of the same arc)

PC = QC (arcs of equal radii)

OC = OC (common)

∴ ∆OPC ≅ ∆OQC (c.p.c.t.)

Consequently, OC is the bisector of ∠AOB.

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Answer 2

Step-by-step explanation:

hope it help u.......................