In Fig., side BC of ∆ABC has been produced to D and CE || BA. If ∠ABC = 65°, ∠BAC = 55°, find ∠ACE, ∠ECD and ∠ACD.

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Solution

$∠$ ABC = $∠$ ECD = 55° (Corresponding angles)
$∠$ BAC = $∠$ ACE = 65° (Alternate interior angles)
Now, $∠$ ACD = $∠$ ACE + $∠$ ECD
⇒ $∠$ ACD = 55° + 65° = 120°

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Similar questions

Q. In the given figure, side BC of

△ A B C

has been produced to D and CE || BA. If

∠ A B C = 65^{o},

∠ B A C = 55^{o},

find

∠ A C E,

and

∠ E C D

respectively.

Q. Mark (✓) against the correct answer
In ∆ABC, side BC has been produced to D such that ∠ACD = 125° and ∠BAC = 60°. Then ∠ABC = ?

(a) 55°
(b) 60°
(c) 65°
(d) 70°

Q. In the given figure, side BC of ∆ABC is produced to D. If ∠ACD = 128° and ∠ABC = 43°, find ∠BAC and ∠ACB.

Q. Mark (✓) against the correct answer
In ∆ABC, side BC has been produced to D. If ∠BAC = 45° and ∠ABC = 55°, then ∠ACD = ?

(a) 80°
(b) 90°
(c) 100°
(d) 110°

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) $75^{\circ}$

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In Fig., side BC of ∆ABC has been produced to D and CE || BA. If ∠ABC = 65°, ∠BAC = 55°, find ∠ACE, ∠ECD and ∠ACD.

∠ABC = ∠ECD = 55° (Corresponding angles) ∠BAC = ∠ACE = 65° (Alternate interior angles) Now, ∠ACD = ∠ACE + ∠ECD ⇒ ∠ACD = 55° + 65° = 120°

$∠$ ABC = $∠$ ECD = 55° (Corresponding angles)
$∠$ BAC = $∠$ ACE = 65° (Alternate interior angles)
Now, $∠$ ACD = $∠$ ACE + $∠$ ECD
⇒ $∠$ ACD = 55° + 65° = 120°