From a point on a line, another line is to be drawn such that the angle on one side is 50° more than the angle on the other side. How much is the smaller angle?

Let's denote the smaller angle by \( x \). According to the problem, the angle on one side of the line is \( 50^\circ \) more than the angle on the other side. Therefore, the larger angle can be expressed as \( x + 50^\circ \).

Since the two angles are formed by a straight line, their sum must be \( 180^\circ \) (because the sum of angles on a straight line is always \( 180^\circ \)).

### Step 1: Write the equation for the sum of the angles.
\[
x + (x + 50^\circ) = 180^\circ
\]

### Step 2: Simplify the equation.
\[
2x + 50^\circ = 180^\circ
\]

### Step 3: Solve for \( x \).
Subtract \( 50^\circ \) from both sides:
\[
2x = 130^\circ
\]
Divide by 2:
\[
x = 65^\circ
\]

### Conclusion:
The smaller angle is \( 65^\circ \).

Would you like more details or have any questions?

Here are some related questions:
1. What would be the smaller angle if the difference was 30° instead of 50°?
2. How would you construct such angles geometrically?
3. What is the relationship between supplementary angles and this problem?
4. How does this concept apply to parallel lines and a transversal?
5. Can you find the larger angle in this scenario?

**Tip:** When dealing with angles on a straight line, always remember that their sum is \( 180^\circ \).

Discover how to find the smaller angle when two angles on a straight line differ by 50 degrees. Follow a step-by-step solution involving the sum of angles on a straight line theorem. Suitable for Grades 7-9 students learning geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation