Question

Given ABC ~ DEF, m<A = 53 degrees, and m<E = 11 degrees, wat is the measure of angle C?

Answer 1

Since ABC ~ DEF, the corresponding angles are congruent. Specifically, angle A in triangle ABC corresponds to angle E in triangle DEF.

Therefore, m<C + m<D + m<E = 180 degrees.

Given that m<A = 53 degrees and m<E = 11 degrees, we can substitute these values into the equation:

m<C + m<D + 11 = 180

We also know that the sum of angles in a triangle is always 180 degrees. Since triangle DEF is a triangle, m<D + m<E + m<F = 180. We can substitute this equation into the previous equation:

m<C + 180 - m<D = 180

Simplifying, we have:

m<C - m<D = 0.

Since m<C - m<D = 0, we can conclude that m<C = m<D.

Therefore, angle C has the same measure as angle D.

Let's call the measure of angle C (and angle D) x.

We have the equation:

x + x + 11 = 180

Combining like terms:

2x + 11 = 180

Subtracting 11 from both sides:

2x = 180 - 11
2x = 169

Dividing both sides by 2:

x = 169/2
x = 84.5

Therefore, the measure of angle C is 84.5 degrees.