Question

1. find the value of x and m∠a.

Explanation:

Step1: Apply 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, \(5x - 27+(7x - 26)=10x - 23\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \((5x+7x)+(-27 - 26)=10x - 23\)
\(12x-53 = 10x - 23\)

Step3: Solve for \(x\)

Subtract \(10x\) from both sides: \(12x-10x-53=10x - 10x - 23\)
\(2x-53=-23\)
Add \(53\) to both sides: \(2x-53 + 53=-23 + 53\)
\(2x=30\)
Divide both sides by \(2\): \(x = 15\)

Step4: Find \(m\angle A\)

Substitute \(x = 15\) into the expression for \(\angle A\) (\(5x-27\))
\(m\angle A=5\times15-27\)
\(m\angle A = 75-27\)
\(m\angle A=48^{\circ}\)

Answer:

\(x = 15\) and \(m\angle A = 48^{\circ}\)