$Side BCof Δ A B C hs been produced to D on left and to E on right-hand side of BC such that ∠ A B D = 125^{\circ} a n d ∠ A C E = 130^{\circ} . T h e n, ∠ A = ?$

$(a) 50^{\circ} (b) 55^{\circ} (c) 65^{\circ} (d) 75^{\circ}$

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Solution

ANSWER:
(d) $75^{\circ}$
We have :
∴ $∠ A B D + ∠ A B C = 180 ° ∵ D E i s a s t r a i g h t l i n e \Rightarrow 125 ° + ∠ A B C = 180 ° \Rightarrow ∠ A B C = 55^{\circ}$
Also,
$∠ A C E + ∠ A C B = 180 ° \Rightarrow 130 ° + ∠ A C B = 180 ° \Rightarrow ∠ A C B = 50 ° ∴ ∠ B A C + ∠ A B C + ∠ A C B = 180^{\circ}$ Sum of the angles of a triangle
⇒ $∠ B A C + 55 ° + 50 ° = 180 ° \Rightarrow ∠ B A C = 75 ° \Rightarrow ∠ A = 75^{\circ}$

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Similar questions

Side $B C$ of $Δ A B C$ has been produced to $D$ on left and to $E$ on right hand side of BC such that $∠ A B D = 125^{\circ}$ and $∠ A C E = 130^{\circ}$ . Then $∠ A =$ ?
(a) $50^{\circ}$
(b) $55^{\circ}$
(c) $65^{\circ}$
(d) $75^{\circ}$

Q. Side BC of ∆ABC has been produced to D on left hand side and to E on right hand side such that ∠ABD = 125° and ∠ACE = 130°. Then ∠A = ?
(a) 65°
(b) 75°
(c) 50°
(d) 55°

$In the given figure, the sides CB and BA of Δ A B C hs been produced to D and E respectively such that ∠ A B D = 110^{\circ} a n d ∠ C A E = 135^{\circ} . T h e n, ∠ A C B = ?$

$(a) 65^{\circ} (b) 45^{\circ} (c) 55^{\circ} (d) 35^{\circ}$

Q. In the given figure, the side

B C

△ A B C

has been produced on the left-hand side from

B

D

and on the right -hand side from

C

E

. if

∠ A B D = 106^{\circ}

and

∠ A C E = 118^{\circ}

, find the measure of each angle of the triangle.

$In the given figure, side BC of Δ A B C has been produced on the left-hand side from B to D and on the right-hand side from C to E. If ∠ A B D = 106^{\circ} a n d ∠ A C E = 118^{\circ}, find the measure of each anlge of the triangle.$

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Side BCof ΔABChs been produced to D on left and to E on right-hand side of BC such that ∠ABD=125∘and ∠ACE=130∘.Then,∠A=? (a)50∘ (b)55∘ (c)65∘ (d)75∘

ANSWER: (d) 75∘ We have : ∴ ∠ABD+∠ABC=180°∵DEisastraightline⇒125°+∠ABC=180°⇒∠ABC=55∘ Also, ∠ACE+∠ACB=180°⇒130°+∠ACB=180°⇒∠ACB=50°∴∠BAC+∠ABC+∠ACB=180∘ Sum of the angles of a triangle ⇒ ∠BAC+55°+50°=180°⇒∠BAC=75°⇒∠A=75∘

$Side BCof Δ A B C hs been produced to D on left and to E on right-hand side of BC such that ∠ A B D = 125^{\circ} a n d ∠ A C E = 130^{\circ} . T h e n, ∠ A = ?$

$(a) 50^{\circ} (b) 55^{\circ} (c) 65^{\circ} (d) 75^{\circ}$