If, overline DM cong overline MC in Delta*DMC and m angle M = 88 deg find m∠C

In \( \triangle DMC \), we are given the following information:

- \( \overline{DM} \cong \overline{MC} \), meaning that triangle \( DMC \) is **isosceles**, with two equal sides \( DM \) and \( MC \).
- \( m \angle M = 88^\circ \), meaning the measure of angle \( M \) is \( 88^\circ \).

### Step-by-step solution:
Since \( \overline{DM} \cong \overline{MC} \), angles opposite these equal sides must also be equal. Therefore:
\[
m \angle D = m \angle C
\]
Let \( m \angle D = m \angle C = x \).

In any triangle, the sum of the angles is always \( 180^\circ \). Therefore, we can set up the following equation:
\[
m \angle D + m \angle M + m \angle C = 180^\circ
\]
Substitute the known values:
\[
x + 88^\circ + x = 180^\circ
\]
Simplify:
\[
2x + 88^\circ = 180^\circ
\]
Solve for \( x \):
\[
2x = 180^\circ - 88^\circ
\]
\[
2x = 92^\circ
\]
\[
x = \frac{92^\circ}{2} = 46^\circ
\]

### Conclusion:
Thus, \( m \angle C = 46^\circ \).

---

Would you like further details on this solution or have any other questions?

Here are 5 related questions you could explore:
1. How do you calculate the angles of a right triangle?
2. What is the property of angles in an equilateral triangle?
3. How does the Pythagorean Theorem apply to isosceles triangles?
4. What happens to the angles when an exterior angle is introduced?
5. Can you apply this method to an obtuse isosceles triangle?

**Tip:** Always remember that in an isosceles triangle, the angles opposite the equal sides are equal!

If, overline DM cong overline MC in Delta DMC and m angle M = 88 deg find m∠C

This geometry problem explores how to find m∠C in an isosceles triangle DMC, given that m∠M = 88° and sides DM and MC are equal. Learn the step-by-step solution using the Angle Sum Property and the Isosceles Triangle 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