Question

d) (14x + 21)° 7x + 3° 46°

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.
So, \(14x + 21=(7x + 3)+46\).

Step2: Simplify the right - hand side

\((7x + 3)+46=7x+(3 + 46)=7x + 49\).
The equation becomes \(14x+21 = 7x + 49\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(14x-7x+21=7x-7x + 49\), which gives \(7x+21 = 49\).
Subtract \(21\) from both sides: \(7x+21-21=49-21\), so \(7x=28\).
Divide both sides by \(7\): \(x=\frac{28}{7}=4\).

Answer:

\(x = 4\)