Find the value of x.  Then find angle GEH if GEH is x+40 and angle DEG is x+30 and angle HEF is 2x+10


We are given three angles:  
- \( \angle GEH = x + 40^\circ \)  
- \( \angle DEG = x + 30^\circ \)  
- \( \angle HEF = 2x + 10^\circ \)

To solve for \( x \), we need to know how these angles relate to each other. Typically, such problems involve angles in a straight line, forming a linear pair, or part of a triangle where the sum of angles is 180°.

### Step-by-Step Solution:

Assuming these angles are on a straight line, such that:
\[
\angle GEH + \angle DEG + \angle HEF = 180^\circ
\]

Substituting the expressions for the angles:
\[
(x + 40) + (x + 30) + (2x + 10) = 180
\]

Simplify the equation:
\[
x + 40 + x + 30 + 2x + 10 = 180
\]
\[
4x + 80 = 180
\]

Solve for \( x \):
\[
4x = 180 - 80
\]
\[
4x = 100
\]
\[
x = \frac{100}{4} = 25
\]

### Finding the Value of \( \angle GEH \):
Now that we know \( x = 25 \), substitute this value into the expression for \( \angle GEH \):
\[
\angle GEH = x + 40 = 25 + 40 = 65^\circ
\]

Thus, \( \angle GEH = 65^\circ \).

---

Would you like more details or explanations on any part of this solution? Here are 5 related questions to deepen your understanding:

1. How do we determine when angles form a straight line?
2. What is the general rule for the sum of angles in a triangle?
3. Can you explain the concept of a linear pair of angles?
4. How does substituting \( x \) into the angle expressions help verify the solution?
5. What would change if these angles were part of a different geometric configuration?

**Tip:** Always check if the angles given form a straight line, a triangle, or another shape, as this determines how their sum behaves!

Find the value of x. Then find angle GEH if GEH is x+40 and angle DEG is x+30 and angle HEF is 2x+10.

Find the value of x and calculate angle GEH given the angle relationships: GEH = x+40, DEG = x+30, and HEF = 2x+10. Learn how to apply the linear pair theorem to solve this geometry problem step-by-step. 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