Question

1. (4 - 48) for each diagram below, write an equation and solve for x.

a. 3x + 3° x + 7°
b. 9x + 4° 3x + 14°

Explanation:

Step1: Identify angle - relationship in part a

The two angles are complementary, so their sum is 90°.
$(3x + 3)+(x + 7)=90$

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+x+3 + 7=90$, which gives $4x+10 = 90$.

Step3: Solve for x

Subtract 10 from both sides: $4x=90 - 10=80$. Then divide both sides by 4: $x=\frac{80}{4}=20$.

Step4: Identify angle - relationship in part b

The two angles are corresponding angles (assuming the lines are parallel), so they are equal.
$9x + 4=3x+14$

Step5: Solve for x in part b

Subtract 3x from both sides: $9x-3x + 4=3x-3x+14$, which gives $6x+4 = 14$. Then subtract 4 from both sides: $6x=14 - 4 = 10$. Divide both sides by 6: $x=\frac{10}{6}=\frac{5}{3}$.

Answer:

a. $x = 20$
b. $x=\frac{5}{3}$