Question

consider △abc. enter the value of x.

Explanation:

Step1: Apply the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
In \(\triangle ABC\), the exterior angle at \(B\) is \(105^{\circ}\), and the two non - adjacent interior angles are \(\angle C = 32^{\circ}\) and \(\angle A=(7x + 3)^{\circ}\). So, \(105=(7x + 3)+32\).

Step2: Simplify the equation

Simplify the right - hand side of the equation: \((7x + 3)+32=7x+(3 + 32)=7x + 35\).
The equation becomes \(105=7x + 35\).

Step3: Solve for \(x\)

Subtract \(35\) from both sides of the equation: \(105-35=7x+35 - 35\).
\(70 = 7x\).
Divide both sides by \(7\): \(\frac{70}{7}=\frac{7x}{7}\).

Answer:

\(x = 10\)