Question

for each diagram below, write an equation and solve for x, if possible.

hint (a):
the two angles are complementary.

hint (b):

Explanation:

Step1: Solve for \(x\) in part (a)

Since the two angles are complementary (\(90^{\circ}\) in total), we have the equation \((3x + 3)+(x + 7)=90\).
Combine like - terms: \(3x+x+3 + 7=90\), which simplifies to \(4x+10 = 90\).
Subtract \(10\) from both sides: \(4x=90 - 10\), so \(4x=80\).
Divide both sides by \(4\): \(x=\frac{80}{4}=20\).

Step2: Solve for \(x\) in part (b)

The two angles are alternate - exterior angles (equal because the lines are parallel), so \(9x + 4=3x+14\).
Subtract \(3x\) from both sides: \(9x-3x + 4=3x-3x + 14\), which gives \(6x+4 = 14\).
Subtract \(4\) from both sides: \(6x=14 - 4\), so \(6x=10\).
Divide both sides by \(6\): \(x=\frac{10}{6}=\frac{5}{3}\approx1.67\).

Answer:

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