Triangle ABC is similar to triangle DEF. If angle A measures 35 degrees and angle E measures 40 degrees, what is the measure of angle C? 35 40 75 105
All triangles have angles that sum to 180 degrees.
So,
Angle C = 180 - 35 - 40
Angle C = 105 degrees
we know that
If triangle ABC is similar to triangle DEF
then
the corresponding angles are equal
∠A=∠D=\(35\°\)
∠B=∠E=\(40\°\)
∠C=∠F
The sum of the internal angles of a triangle is equal to \(180\°\)
so
In the triangle ABC
∠A+∠B+∠C= \(180\°\)
Substitute the values and solve for ∠C
∠C= \(180\°-35\°-40\°=105\°\)
therefore
the answer is
The measure of angle C is \(105\°\)