Question

1. the measure of an angle is four - times the measure of its supplementary angle. what is the measure of each angle? 9. find the value of x. 10. find the value of x.

Explanation:

Step1: Define supplementary angles

Supplementary angles add up to 180°. Let one angle be $x$, then its supplementary angle is $180 - x$. Given that $x = 4(180 - x)$.

Step2: Solve the equation

Expand the right - hand side: $x=720 - 4x$. Add $4x$ to both sides: $x + 4x=720$, so $5x = 720$. Divide both sides by 5: $x=\frac{720}{5}=144$. The other angle is $180 - 144 = 36$.

Step3: Analyze problem 9

The sum of angles around a point is 360°. So, $3x+90 + 26+x=360$. Combine like terms: $4x+116 = 360$. Subtract 116 from both sides: $4x=360 - 116=244$. Divide by 4: $x = 61$.

Step4: Analyze problem 10

Vertical angles are equal. So, $45=5x + 7$. Subtract 7 from both sides: $45-7 = 5x$, so $38 = 5x$. Divide by 5: $x=\frac{38}{5}=7.6$.

Answer:

1. 144, 36
2. 61
3. 7.6