Question

Suppose △ABC≅△DEF, m∠B=76° , and m∠D=59° .

What is m∠F?




a. 104º

b. 76º

c. 59º

d. 45º

Answer 1

Hello!

This equation shows that ΔABC is approximately equal to to ΔDEF. This means that the angles are the same. We will subtract both angles from 180 to find m∠F.

180-76-56=45.

Therefore our answer is D) 45°.

I hope this helps!

Answer 2

Answer: d. 45º

Explanation:

Given : ΔABC≅ ΔDEF

⇒ Corresponding angles of ΔABC and ΔDEF are congruent. ( corresponding parts of congruent triangles are congruent.)

Also, the congruent angles has the same measure.

⇒m∠A=m∠D=59°

m∠B=m∠E=76°

m∠C=m∠F

Now in ΔDEF , we have

m∠D+m∠E+m∠F=180° [By Angle sum property of triangle]

⇒59°+76°+m∠F=180° [Substitute values of m∠D and m∠E]

⇒135°+m∠F=180°

⇒m∠F=180°-135°

⇒m∠F=45°

Hence, d is the correct answer.