If triangle ABC is similar to triangle DEF, angle A is equal to 46 degrees, and angle E is equal to 62 degrees. Is the measure of angle C equal to 72 degrees? Give a reason.

The assertion that Angle C equals 72 degrees in a triangle ABC that is similar to triangle DEF, with known angles A=46 and E=62, is true. The conclusion leverages the fact that the sum of all angles in a triangle equals 180 degrees.

Explanation:

In this case, the question refers to similar triangles. Similar triangles are those that have the same shape but may differ in size. The key property of similar triangles is that their corresponding angles are equal.

If triangle ABC is similar to triangle DEF, this implies that Angle A is equal to Angle D, Angle B is equal to Angle E, and Angle C must be equal to Angle F. Now if Angle A is given as 46 degrees and Angle E as 62 degrees, the third angle in each triangle (Angles C and F) can be found by realizing that the sum of all angles in a triangle is 180 degrees.

So, Angle C in triangle ABC will be 180 - (46 + 62) = 72 degrees. Hence, if the assertion is that Angle C equals 72 degrees, then it is true. This is because it matches the calculation based on the fact that the sum of all angles in a triangle should amount to 180 degrees.

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