If in the triangles $A B C$ and $D E F$ , angle $A$ is equal to angle $E$ , both are equal to $40^{o}$ , $A B : E D = A C : E F$ and angle $F$ is $65^{o}$ , then angle $B$ is:

35^{o}

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65^{o}

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75^{o}

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85^{o}

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Solution

The correct option is B $75^{o}$
In $△ A B C$ and $△ E D F$
$∠ A = ∠ E$
$\frac{A B}{E D} = \frac{A C}{E F}$
Thus, $△ A B C \sim △ E D F$
Thus, $∠ C = ∠ F = 65$
Also, $∠ A = 40$
Now, in $△ A B C$
$∠ A + ∠ B + ∠ C = 180$
$∠ B = 180 - 40 - 65$
$∠ B = 75$

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Similar questions

Q. If in

△

A B C

and

D E F,

∠ A = ∠ E = 37^{\circ}, A B : E D = A C : E F

and

∠ F = 69^{\circ},

then what is the value of

∠ B ?

If in the $△$ 's ABC and DEF, $∠$ A is equal to $∠$ E, both are equal to $40^{\circ}$ . AB : ED = AC : EF and angle F is $65^{\circ}$ , then angle B is:

Q. In triangles ABC and DEF, ∠A = ∠E = 40°, AB : ED = AC : EF and ∠F = 65°, then ∠B =

(a) 35°
(b) 65°
(c) 75°
(d) 85°

Q. In a triangle if two angles are

85^{o}

and

75^{o}

then the other angle is

Q. If in ∆ABC and ∆DEF,

\frac{AB}{DE} = \frac{BC}{FD}

, then ∆ABC ∼ ∆DEF when

(a) ∠A = ∠F
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠B = ∠E

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If in the triangles ABC and DEF, angle A is equal to angle E, both are equal to 40o, AB:ED=AC:EF and angle F is 65o, then angle B is:

The correct option is B 75oIn △ABC and △EDF ∠A=∠E ABED=ACEFThus, △ABC∼△EDF Thus, ∠C=∠F=65Also, ∠A=40Now, in △ABC ∠A+∠B+∠C=180 ∠B=180−40−65 ∠B=75

If in the triangles $A B C$ and $D E F$ , angle $A$ is equal to angle $E$ , both are equal to $40^{o}$ , $A B : E D = A C : E F$ and angle $F$ is $65^{o}$ , then angle $B$ is:

The correct option is B $75^{o}$
In $△ A B C$ and $△ E D F$
$∠ A = ∠ E$
$\frac{A B}{E D} = \frac{A C}{E F}$
Thus, $△ A B C \sim △ E D F$
Thus, $∠ C = ∠ F = 65$
Also, $∠ A = 40$
Now, in $△ A B C$
$∠ A + ∠ B + ∠ C = 180$
$∠ B = 180 - 40 - 65$
$∠ B = 75$