Question

for questions 5 and 6, find the value of x.
5.
6.

Explanation:

Question 5

Step1: Use the triangle angle - sum property

The sum of interior angles of a triangle is \(180^{\circ}\). So, \((6x - 30)+(6x - 5)+(2x - 1)=180\).

Step2: Simplify the left - hand side

Combine like terms: \((6x+6x + 2x)+(-30-5 - 1)=180\), which is \(14x-36 = 180\).

Step3: Solve for \(x\)

Add \(36\) to both sides: \(14x=180 + 36=216\). Then divide both sides by \(14\): \(x=\frac{216}{14}=\frac{108}{7}\approx15.43\).

Question 6

Step1: Use the exterior angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \((5x - 14)+(7x + 26)=10x-6\).

Step2: Simplify the left - hand side

Combine like terms: \(5x+7x-14 + 26=10x-6\), which is \(12x + 12=10x-6\).

Step3: Solve for \(x\)

Subtract \(10x\) from both sides: \(12x-10x+12=10x-10x - 6\), so \(2x+12=-6\). Subtract \(12\) from both sides: \(2x=-6 - 12=-18\). Divide both sides by \(2\): \(x=-9\).

Answer:

Question 5: \(x = \frac{108}{7}\)
Question 6: \(x=-9\)