Question

1. given that lines s and t are perpendicular, find the value of x:

(3x + 5)°
40°
a. 15
b. 50
c. 45
d. 12

1. given that lines s and t are perpendicular, find the value of x:

5x°
10x°
a. 6
b. 15
c. 90
d. 2

Explanation:

Question 5

Step1: Use perpendicular lines property

Since lines \(s\) and \(t\) are perpendicular, the sum of \((3x + 5)^{\circ}\) and \(40^{\circ}\) is \(90^{\circ}\). So, \(3x+5 + 40=90\).

Step2: Simplify the equation

Simplify the left - hand side: \(3x+45 = 90\).

Step3: Solve for \(x\)

Subtract \(45\) from both sides: \(3x=90 - 45\), so \(3x = 45\). Then divide both sides by \(3\): \(x=\frac{45}{3}=15\).

Step1: Use perpendicular lines property

Since lines \(s\) and \(t\) are perpendicular, the sum of \(5x^{\circ}\) and \(10x^{\circ}\) is \(90^{\circ}\). So, \(5x+10x = 90\).

Step2: Simplify the equation

Combine like terms: \(15x=90\).

Step3: Solve for \(x\)

Divide both sides by \(15\): \(x=\frac{90}{15}=6\).

Answer:

A. 15

Question 6