△ = Triangle
If △ABC is similar to △DEF, and angle A is 62 degrees, angle B is 13 degrees, find the measure of angle F.
(Also I don't want just the answer, I also want to know how to actually do it so I will know how to do this.)
if A is 62, so is D
If B is 13, so is E
So, since D+E+F=180, just plug in your values for D and E.
To find the measure of angle F in △DEF, given that △ABC is similar to △DEF, angle A is 62 degrees, and angle B is 13 degrees, you can use the concept of corresponding angles in similar triangles.
In similar triangles, corresponding angles are equal. This means that angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.
Since angle A is given as 62 degrees, we can conclude that angle D (which corresponds to angle A) is also 62 degrees.
Similarly, since angle B is given as 13 degrees, angle E (which corresponds to angle B) is also 13 degrees.
Now, to find the measure of angle F, we need to use the fact that the sum of the angles in any triangle is always 180 degrees. So, we can subtract the known angles from 180 degrees:
Angle F = 180 degrees - angle C
Since angle C corresponds to angle F, angle C is the same as angle F. Therefore,
Angle F = 180 degrees - angle C = 180 degrees - angle B = 180 degrees - 13 degrees
By subtracting 13 degrees from 180 degrees, we get:
Angle F = 167 degrees
Therefore, the measure of angle F is 167 degrees in △DEF.