Question

1. 6) 43° (x - 4)° 70° (6x + 1)° (3x + 2)° page 1 / 4

Explanation:

Step1: Identify vertical - angle relationship

In problem 5, vertical angles are equal. So, $6x + 1=43$.

Step2: Solve the equation for $x$

Subtract 1 from both sides: $6x=43 - 1=42$. Then divide both sides by 6: $x=\frac{42}{6}=7$.

Step3: Identify angle - sum relationship in problem 6

The sum of the angles around a point is $360^{\circ}$. So, $(x - 4)+70+(3x + 2)=360$.

Step4: Simplify the left - hand side of the equation

Combine like terms: $x-4 + 70+3x + 2=4x+68$.

Step5: Solve the equation for $x$

Set $4x+68 = 360$. Subtract 68 from both sides: $4x=360 - 68=292$. Then divide both sides by 4: $x=\frac{292}{4}=73$.

Answer:

For problem 5: $x = 7$
For problem 6: $x = 73$