Question

Find x in the following case:

Answer 1

Step 1: Analyze the situation

• The angle 4x and 130^∘ form a linear pair, which means their sum is 180^∘.
• Similarly, the angle 130^∘ and 6x also form a linear pair, and their sum is 180^∘.

Step 2: Write equations

1. For the first linear pair: 4x + 130 = 180

2. For the second linear pair: 130 + 6x = 180

Step 3: Solve each equation for x

Equation 1: 4x + 130 = 180

Subtract 130 from both sides

4x = 50

Divide by 4

x = 12.5

Equation 2: 130 + 6x = 180 

Subtract 130 from both sides

6x = 50

Divide by 6: x = 8.33

If both equations correspond to the same x, recheck the linearity of the situation with complementary supplement.