6.1 Foundations: Lines, Rays, and Angle Intuition

Step 1

Since $\angle A$ and $\angle B$ form a linear pair, their sum is $180^\circ$ (Axiom 6.1).

Step 2

Equation: $(2x + 10) + (3x - 30) = 180$ .

Step 3

Simplify: $5x - 20 = 180$ .

Step 4

$5x = 200 \implies x = 40$ .

Step 5

Calculate angles: $\angle A = 2(40) + 10 = 90^\circ$ , $\angle B = 3(40) - 30 = 90^\circ$ .

Final Answer

$x=40, \angle A = 90^\circ, \angle B = 90^\circ$

Operation

Angle 1 (degrees)

Select operation and enter angles.