Triangle ABC is similar to triangle DEF. If angle A measures 28 degrees and angle B measures 74 degrees. If angle F is the largest angle in triangle DEF, what is the measure of angle F?

Since the angles of a triangle have to add up to 180 degrees, and angle A is 28 degrees, and angle B is 74 degrees, angle C would have to be 78 degrees so there are a total of 180 degrees in the triangle. Since triangle ABC is similar to triangle DEF, the angle measurements of that triangle would also have to be 28 degrees, 74 degrees, and 78 degrees, corresponding to angles D, E, and F. Since the largest of these numbers is 78 degrees, and angle F is the largest angle of the triangle, that would be your answer.

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shrutiagrawal1798 shrutiagrawal1798 · Answer 2 · 2021-11-18T16:47:51+01:00

The triangle is three sided polygon which have three vertices and three edges. If a triangle has three vertices A, B and C then it can be represent as [tex]\Delta ABC[/tex] .

The measure of angle [tex]F[/tex] is [tex]78^{\circ}[/tex].

Given:

Angle [tex]\angle A=28^{\circ}[/tex]

Angle [tex]\angle B=74^{\circ}[/tex]

As per the problem triangle ABC and triangle DEF similar. As per the property of triangle if two triangle are similar then their angle would be congruent.

[tex]\angle A=\angle D=28^{\circ}\\\angle B=\angle E=74^{\circ}\\\angle C=\angle F=?[/tex]

As we the know that sum of three angle of triangle is [tex]180^{\circ}[/tex].

[tex]\angle D+\angle E+\angle F=180^{\circ}\\28^{\circ}+74^{\circ}+\angle F=180^{\circ}\\\angle F=78^{\circ}[/tex]

Thus, the measure of angle [tex]F[/tex] is [tex]78^{\circ}[/tex].

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