Question

In triangle ABC point P and Q on sides AB and AC are such that AP÷PB= AQ÷QC .if PQ is extended to T such that PT = BC and PB = TC then find the value of x​

Answer 1

Answer:

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Step-by-step explanation:

aqp=tqc vertically opp angles

apq=qtc alternate interior angles

tqc+qtc+qct=180 angle sum property

qct=x

x=60

Answer 2

Given :- In triangle ABC point P and Q on sides AB and AC are such that AP/PB = AQ/QC .if PQ is extended to T such that PT = BC and PB = TC . Find the value of ∠QTC ?

Solution :-

we have,

→ AP / PB = AQ / QC .

so,

→ PQ || BC . (By converse of BPT.)

then,

→ PT || BC and PT = BC (given) .

also,

→ PB || TC and PB = TC (given) .

therefore,

• PBCT is a ll gm. { Opposite sides are parallel and equal. }

now,

→ ∠ABC = ∠APQ { Corresponding angles. }

→ ∠ABC = 45° .

hence,

→ ∠PTC = ∠PBC { Opposite angles of a ll gm are equal. }

→ ∠PTC = 45°

→ ∠QTC = 45° (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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