Question

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the diagram shows a triangle. what is the value of x?

Explanation:

Step1: Apply the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 14)+(4x + 20)+(x + 20)=180\).

Step2: Combine like terms

First, expand the left - hand side: \(x+14 + 4x+20+x + 20=(x + 4x+x)+(14 + 20+20)=6x+54\).
So the equation becomes \(6x+54 = 180\).

Step3: Solve for \(x\)

Subtract 54 from both sides of the equation: \(6x=180 - 54\), which gives \(6x=126\).
Then divide both sides by 6: \(x=\frac{126}{6}\).

Answer:

\(x = 21\)