(C) In $\Delta DEF$,the sum of angles is $180^{\circ}$.Given $m \angle E + m \angle F = 130^{\circ}$.Therefore,$m \angle D = 180^{\circ} - (m \angle E

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(C) In $\Delta DEF$,the sum of angles is $180^{\circ}$.Given $m \angle E + m \angle F = 130^{\circ}$.Therefore,$m \angle D = 180^{\circ} - (m \angle E + m \angle F) = 180^{\circ} - 130^{\circ} = 50^{\circ}$.Since the correspondence $ABC \leftrightarrow FDE$ represents a similarity,the corresponding angles are equal.Specifically,$\angle B$ corresponds to $\angle D$.Therefore,$m \angle B = m \angle D = 50^{\circ}$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow FDE$. If $m \angle E + m \angle F = 130^{\circ}$,then $m \angle B = \dots$ (in $^{\circ}$)

A
$65$
B
$130$
C
$50$
D
$100$

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Mix Examples - Triangles

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $BD = 2.5$,$AB = 5$ and $AC = 4.2$,find $DC$.

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The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

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$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow FDE$. If $m \angle E + m \angle F = 130^{\circ}$,then $m \angle B = \dots$ (in $^{\circ}$)

Similar Questions

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $BD = 2.5$,$AB = 5$ and $AC = 4.2$,find $DC$.

In $\Delta ABC$,$m\angle B = 90^\circ$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 4CM$,prove that $AB = 2BC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. Prove that $\frac{AB^2}{BC^2} = \frac{AM}{CM}$.

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The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

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