Question

In the given figure, PQ II RS and angle ACS = 127 degrees, find angle BAC ​

Answer 1

Answer:127°

Step-by-step explanation:

we all know that in triangle sum of all angle is 180°

∠BAS + ∠ACS = 180°

∠BAS + 127° = 180°

         ∠BAS = 180 - 127

          ∠BAS = 53°      

Answer 2

Given :- PQ II RS and ∠ACS = 127° . Also, ∠PAB = 50° { from image . }

To Find :- ∠BAC = ?

Solution :-

Basic Method :-

→ ∠ACS + ∠ACB = 180° { Linear pair }

→ 127° + ∠ACB = 180°

→ ∠ACB = 180° - 127°

→ ∠ACB = 53° ---------- Eqn.(1)

also,

→ ∠PAB = ∠ABC { Alternate interior angles }

→ ∠ABC = 50° ------------ Eqn.(2)

now, in ∆ABC we have,

→ ∠ABC + ∠ACB + ∠BAC = 180° { By angle sum property. }

putting values from Eqn.(1) and Eqn.(2),

→ 50° + 53° + ∠BAC = 180°

→ 103° + ∠BAC = 180°

→ ∠BAC = 180° - 103°

→ ∠BAC = 77° (Ans.)

Short Method :-

→ ∠PAB = ∠ABC { Alternate interior angles }

→ ∠ABC = 50°

now,

→ ∠ABC + ∠BAC = ∠ACS { Exterior angle is equal to sum of opposite interior angles.}

→ 50° + ∠BAC = 127°

→ ∠BAC = 127° - 50°

→ ∠BAC = 77° (Ans.)

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