Question

Find measure of angles B, E, D and C and the length of BC.

Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.

Answer 1

< B = 180-30-65=85°

< E = 85°

< D = 30°

< C = 65°

BC = 20/35 × 28 = 16

Answer 2

<D = 30

< C = 65

<B = <E = 85

16 = BC

Explanation:

ABC ~ Triangle DEF

<A = <D = 30

< C = <F = 65

Since they are similar triangles

A+ C + B = 180 since the angles of a triangle = 180

30+65+B =180

95+ B = 180

<B = 180 -95 = 85

<B = <E = 85

The triangles are similar so the sides are proportional

AB BC

---- = ---------

DE EF

20 BC

---- = ---------

35 28

Using cross products

20*28 = 35 BC

Divide each side by 35

20*28/35 = 35/35 BC

16 = BC