Question

angle pairs
find the value of x and the measure of angles 1 - 6
variable value result
x ×
1 ×
2 ×
3 ×
4 ×
5 ×
6 ×

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(19x+6x = 85\) (since \(85^{\circ}\) is equal to the sum of the angles with measures \(19x\) and \(6x\) as they are vertical - angle related).

Step2: Solve for x

Combine like terms: \(25x=85\), then \(x = \frac{85}{25}= 3.4\) (This is wrong. Let's start over. The correct relationship is that \(19x\) and \(6x\) are adjacent angles to the \(85^{\circ}\) angle and form a straight - line, so \(19x + 6x+85=180\)).

Step3: Correct equation and solve for x

Combine like terms: \(25x=180 - 85\), \(25x = 95\), \(x=\frac{95}{25}=5\).

Step4: Find angle 2

Angle 2 has measure \(6x\). Substitute \(x = 5\), so \(\angle2=6\times5 = 30^{\circ}\).

Step5: Find angle 1

Angle 1 and angle 2 are vertical angles. So \(\angle1=\angle2 = 30^{\circ}\).

Step6: Find angle 3

Angle 3 and angle 1 are vertical angles. So \(\angle3=\angle1 = 30^{\circ}\).

Step7: Find angle 5

Angle 5 and the \(85^{\circ}\) angle are vertical angles. So \(\angle5 = 85^{\circ}\).

Step8: Find angle 4

Angle 4 and angle 5 are adjacent and form a straight - line. So \(\angle4=180 - 85=95^{\circ}\).

Step9: Find angle 6

Angle 6 and angle 4 are vertical angles. So \(\angle6=\angle4 = 95^{\circ}\).

Answer:

• x: 5
• 1: 30°
• 2: 60°
• 3: 30°
• 4: 95°
• 5: 85°
• 6: 95°