Question

In △ABC , m∠B=140° and m∠C=10° . In △DEF , m∠D=30° and m∠F=10° .

Which statement about the triangles is true?
(a) △ABC is not similar to △DEF .
(b) △ABC is similar to △DEF
(c) Not enough information is given to determine if △ABC is similar to △DEF

Answer 1

(b) △ABC is similar to △DEF

In △ABC the only angle missing is 30 due to the fact all angles in a triangle add up to 180. So 140+10+(30)=180 and (30)+(10)+140=180

Answer 2

(B) △ABC is similar to △DEF

Explanation:

It is given that In △ABC , m∠B=140° and m∠C=10° . In △DEF , m∠D=30° and m∠F=10°.

Now, in △ABC, using the angle sum property, we have

m∠A+m∠B+m∠C=180°

⇒m∠A+140+10=180

⇒m∠A=30°.

Now, from △ABC and △DEF, we have

m∠A=m∠D=30°(Proved above)

m∠C=m∠F=10°(Given)

Thus, by AA similarity,

△ABC is similar to △DEF

Therefore, option B is correct that is △ABC is similar to △DEF.