Question

the diagram shows a triangle.
a-12°
2a+1°
2a-19°
what is the value of a?
a = □°

Explanation:

Step1: Sum of triangle angles is \(180^\circ\)

The three angles are \(a - 12^\circ\), \(2a + 1^\circ\), and \(2a - 19^\circ\). So, \((a - 12) + (2a + 1) + (2a - 19) = 180\).

Step2: Simplify the equation

Combine like terms: \(a + 2a + 2a - 12 + 1 - 19 = 180\) → \(5a - 30 = 180\).

Step3: Solve for \(a\)

Add 30 to both sides: \(5a = 210\). Divide by 5: \(a = \frac{210}{5} = 42\).

Answer:

\(42\)