Question

1. find the value of x. show work.

( mangle cad = 12x + 4 ) ( mangle b = 4x + 10 )

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(\angle CAD\) is an exterior angle of \(\triangle ABC\), so \(m\angle CAD=m\angle B + m\angle C\).
Substitute the given expressions: \(12x + 4=(4x + 10)+26\).

Step2: Simplify the right - hand side

Simplify \((4x + 10)+26\) to get \(4x+36\). So the equation becomes \(12x + 4=4x + 36\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(12x-4x + 4=4x-4x + 36\), which simplifies to \(8x+4 = 36\).
Subtract \(4\) from both sides: \(8x+4 - 4=36 - 4\), so \(8x=32\).
Divide both sides by \(8\): \(x=\frac{32}{8}\).

Answer:

\(x = 4\)