Question

geometry: section 2 2nd 9 weeks
monday 11/1/21 quiz 3.1 - 3.2
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question 1 (1 point)
find the value of the variable, given ( p perp q ).
( y=)
blank 1:
question 2 (1 point)
find the value of the variable, given ( k n perp n l )
( y=)
blank 1:
question 3 (1 point)
of 3

Explanation:

Question 1

Step1: Use the property of perpendicular lines

Since \(p\perp q\), the angle formed is \(90^{\circ}\). So, \(3y - 12=90\).

Step2: Solve the equation for \(y\)

Add \(12\) to both sides: \(3y=90 + 12=102\). Then divide both sides by \(3\): \(y=\frac{102}{3}=34\).

Question 2

Step1: Use the property of perpendicular lines and angle relationships

Since \(KN\perp NL\), \(\angle KNL = 90^{\circ}\). The given angle \(40^{\circ}\) and \((9y - 4)^{\circ}\) are complementary (they add up to \(90^{\circ}\)). So, \(40+(9y - 4)=90\).

Step2: Simplify the left - hand side of the equation

\(40+9y-4=90\), which simplifies to \(9y + 36=90\).

Step3: Solve for \(y\)

Subtract \(36\) from both sides: \(9y=90 - 36 = 54\). Then divide both sides by \(9\): \(y=\frac{54}{9}=6\).

Answer:

Question 1: \(34\)
Question 2: \(6\)