Question

Given Triangle ABC ~ Triangle DEF, Mesaurement Angle A= 52 and Mesurement Angle E= 11 What is the Mesure of angle C

Answer 1

In similar triangles, the corresponding angles are equal. Since \( \triangle ABC \sim \triangle DEF \), the corresponding angles \( A \) and \( E \) are related. We know:

- \( \text{Measure of Angle A} = 52^\circ \)
- \( \text{Measure of Angle E} = 11^\circ \)

To find the measure of angle \( C \) in triangle \( ABC \), we first need to determine angle \( F \) in triangle \( DEF \). In a triangle, the sum of the angles is always \( 180^\circ \). Thus, we can find angle \( F \) as follows:

\[
\text{Measure of Angle F} = 180^\circ - \text{Measure of Angle E} - \text{Measure of Angle D}
\]

Since we do not have the value of angle \( D \), we can't find angle \( F \) directly. However, we can find angle \( C \) by recognizing the relationship between the angles.

We know that in similar triangles:

\[
\text{Measure of Angle A} + \text{Measure of Angle B} + \text{Measure of Angle C} = 180^\circ
\]

Since we already have \( \text{Measure of Angle A} = 52^\circ \), we can express it as:

\[
52^\circ + \text{Measure of Angle B} + C = 180^\circ
\]

Let's assume that Angle \( B \) corresponds to angle \( E \):

\[
\text{Measure of Angle B} = \text{Measure of Angle E} = 11^\circ
\]

Now, substituting this into the equation gives:

\[
52^\circ + 11^\circ + C = 180^\circ
\]

Now, simplifying this:

\[
63^\circ + C = 180^\circ
\]

Thus:

\[
C = 180^\circ - 63^\circ = 117^\circ
\]

So, the measure of angle \( C \) is \( 117^\circ \).