Question

question image
p
d
b
c
84°
17x - 1
7x + 5
o. solve for x

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(17x - 1=(7x + 5)+84\)

Step2: Simplify the right - hand side

Simplify \((7x + 5)+84\) to get \(7x+89\). So the equation becomes \(17x - 1=7x + 89\)

Step3: Subtract \(7x\) from both sides

\(17x-7x - 1=7x-7x + 89\), which simplifies to \(10x-1 = 89\)

Step4: Add 1 to both sides

\(10x-1 + 1=89 + 1\), so \(10x=90\)

Step5: Divide both sides by 10

\(\frac{10x}{10}=\frac{90}{10}\), which gives \(x = 9\)

Answer:

\(x = 9\)