Question

If triangle ABC is similar to triangle DEF , angle A=30, angle c=50,AB=5cm
AC=8cm,DF=19.2cm .Then which of the following is true
A) angle E=50,DF=12cm
B) angle D=30,EF=12cm
C) angle E=100,DE=12cm
D) angle D=100,EF=12cm​

Answer 1

Answer:

correct alternative is C angle E=100,DE=12cm

Answer 2

C)Angle E=100 degree and DE=12 cm

Step-by-step explanation:

Triangle ABC is similar to triangle DEF

Angle A=30 degrees

Angle C=50 degrees

AB=5 cm,AC=8 cm,DF=19.2 cm

We know that when two triangle are similar then their corresponding angles are equal and the ratio of corresponding sides are equal.

$\angle A=\angle D,\angle B=\angle E,\angle C=\angle F$

Angle D=30 degrees

Angle F=50 degrees

In triangle ABC

$\angle A+\angle B+\angle C=180^{\circ}$

Using triangle angles sum property

$30+50+\angle B=180$

$80+\angle B=180$

$\angle B=180-80=100^{\circ}$

Angle E=100 degrees

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

$\frac{5}{DE}=\frac{8}{19.2}$

$DE=\frac{5\times 19.2}{8}=12cm$

Hence, Angle E=100 degree and DE=12 cm

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