Problem Analysis:
The given image shows a triangle \( \triangle DEF \) with the following information:
- \( \angle D = 72^\circ \)
- \( \angle F = 48^\circ \)
- We are asked to find the measure of \( \angle E \).
Step-by-Step Solution:
1.
Sum of Angles in a Triangle:
The sum of the interior angles in any triangle is always \( 180^\circ \). This is a fundamental property of triangles.
Mathematically, for \( \triangle DEF \):
\[
\angle D + \angle E + \angle F = 180^\circ
\]
2.
Substitute the Given Angles:
We are given:
\[
\angle D = 72^\circ \quad \text{and} \quad \angle F = 48^\circ
\]
Substitute these values into the equation:
\[
72^\circ + \angle E + 48^\circ = 180^\circ
\]
3.
Simplify the Equation:
Combine the known angle measures:
\[
72^\circ + 48^\circ = 120^\circ
\]
So the equation becomes:
\[
120^\circ + \angle E = 180^\circ
\]
4.
Solve for \( \angle E \):
Subtract \( 120^\circ \) from both sides of the equation:
\[
\angle E = 180^\circ - 120^\circ
\]
\[
\angle E = 60^\circ
\]
Final Answer:
The measure of \( \angle E \) is:
\[
\boxed{60^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of triangle missing.
