In triangle ABC, the measure of angle A is 30 degrees. In triangle DEF the measure of angle F is 60 dredgers. Find the rest of the angle measures in each triangle and compare them

Hence In ΔABC  ∠B= 90 and ∠C= 60 and ΔDEF  ∠D= 30 and ∠E=90

(units are in degrees)

Step-by-step explanation:

Given:

Two triangles ABC and DEF has to similar triangles

(otherwise there is no way to find 2 angles of triangle with one angle given and no other relationship)

To Find:

Remaining angles of the two triangles.

Solution:

Two triangles  to be  the similar or congruent  it implies that

ABC≅DEF

∠A=∠D  ∠B=∠E

and ∠C=∠F

Hence ∠A=30

i.e ∠D=30 degree.

∠F=60

i.e.∠C=60 degree.

Now

Sum of all angles of triangle is 180

∠A+∠B+∠C=180

30+∠B+60=180

∠B=180-90

∠B=90

Therefore angle B is 90 degree.

Hence ∠E=90 degree

And ∠D=180-∠E-∠F=30 degree.

Angle D=30 degree.

check the picture below.