Question

In a pair of supplementary angles, the greater angle exceeds the smaller by $50^\circ$. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

Hint:

Translate real-life conditions into linear equations for systematic solving.

Answer 1

Problem:
Two supplementary angles differ by 50°. Determine the measures of both angles.

Step 1: Define variables
Let the smaller angle be \( x^\circ \). Therefore, the larger angle is \( x + 50^\circ \).

Step 2: Apply the supplementary angle property
Supplementary angles sum to \( 180^\circ \). Thus:\[x + (x + 50) = 180 \quad \text{(Equation 1)}\]
Step 3: Simplify the equation
\[x + x + 50 = 180\\2x + 50 = 180\]
Step 4: Solve for \( x \)
\[2x = 180 - 50 = 130\\x = \frac{130}{2} = 65\]
Step 5: Calculate the greater angle
\[y = x + 50 = 65 + 50 = 115\]
Final Answer:
Smaller angle = \( \boxed{65^\circ} \)
Greater angle = \( \boxed{115^\circ} \)