Question

day 5 - friday, september 19th
\\(\angle10=(x + 40)^{circ},\angle11=(2x + 10)^{circ}\\).
state their angle relationship.
solve for x.
find \\(\angle10\\) and \\(\angle11\\).

Explanation:

Step1: Assume supplementary angles

If we assume that $\angle10$ and $\angle11$ are supplementary (since no other relationship - hint is given and this is a common scenario in angle - problems), then $\angle10+\angle11 = 180^{\circ}$.
$(x + 40)+(2x + 10)=180$

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side of the equation.
$x+2x+40 + 10=180$
$3x+50 = 180$

Step3: Isolate the variable term

Subtract 50 from both sides of the equation.
$3x=180 - 50$
$3x=130$

Step4: Solve for x

Divide both sides of the equation by 3.
$x=\frac{130}{3}\approx43.33$

Step5: Find $\angle10$

Substitute $x=\frac{130}{3}$ into the expression for $\angle10$.
$\angle10=x + 40=\frac{130}{3}+40=\frac{130 + 120}{3}=\frac{250}{3}\approx83.33^{\circ}$

Step6: Find $\angle11$

Substitute $x=\frac{130}{3}$ into the expression for $\angle11$.
$\angle11=2x + 10=2\times\frac{130}{3}+10=\frac{260}{3}+10=\frac{260+30}{3}=\frac{290}{3}\approx96.67^{\circ}$

Answer:

• Angle relationship: Supplementary (assumed).
• $x=\frac{130}{3}$
• $\angle10=\frac{250}{3}^{\circ}$
• $\angle11=\frac{290}{3}^{\circ}$