In triangle, E, F, G, comma△EFG, start overline, F, G, end overline, \cong, start overline, E, F, end overline 
FG
 ≅ 
EF
  and m, angle, E, equals, 11, degrees, .m∠E=11 
∘
 . Find m, angle, G, .m∠G.

We are given a triangle \( \triangle EFG \) where:

- \( \overline{FG} \cong \overline{EF} \), meaning sides \( FG \) and \( EF \) are congruent.
- \( m\angle E = 11^\circ \), meaning angle \( E \) measures \( 11^\circ \).

### Step 1: Recognize that the triangle is isosceles.
Since \( \overline{FG} \cong \overline{EF} \), triangle \( \triangle EFG \) is isosceles, with the base being side \( EG \). In an isosceles triangle, the angles opposite the equal sides are also congruent. Therefore:

\[
m\angle G = m\angle F
\]

### Step 2: Use the sum of angles in a triangle.
The sum of the interior angles of any triangle is \( 180^\circ \). Therefore, we have the following equation:

\[
m\angle E + m\angle F + m\angle G = 180^\circ
\]

Since \( m\angle F = m\angle G \), we can rewrite this as:

\[
11^\circ + 2m\angle G = 180^\circ
\]

### Step 3: Solve for \( m\angle G \).
Subtract \( 11^\circ \) from both sides:

\[
2m\angle G = 169^\circ
\]

Now, divide by 2:

\[
m\angle G = \frac{169^\circ}{2} = 84.5^\circ
\]

Thus, the measure of \( \angle G \) is \( 84.5^\circ \).

### Final Answer:
\[
m\angle G = 84.5^\circ
\]

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. What are the properties of isosceles triangles?
2. How do you find the third angle in a triangle if two angles are known?
3. Can an isosceles triangle have angles greater than \( 90^\circ \)?
4. How does the Pythagorean theorem apply to isosceles triangles?
5. How can you use trigonometry to find side lengths in an isosceles triangle?

**Tip:** Always remember the sum of angles in any triangle is \( 180^\circ \), a fundamental rule in geometry!

In triangle EFG, \( \overline{FG} \cong \overline{EF} \) and \( m\angle E = 11^\circ \). Find \( m\angle G \).

Solve for the angle \( G \) in triangle EFG, where \( FG \cong EF \) and \( m\angle E = 11^\circ \). This problem explores the properties of isosceles triangles and uses the triangle angle sum theorem. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation