Question

24 ∠1 = x°, ∠2 = x + 20°, ∠3 = 2x - 10° → find ∠3 angle 3 =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle1+\angle2+\angle3 = 180^{\circ}\).
Substitute \(\angle1=x^{\circ}\), \(\angle2=(x + 20)^{\circ}\), and \(\angle3=(2x-10)^{\circ}\) into the equation:
\(x+(x + 20)+(2x-10)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(x+x+2x+20 - 10=180\)
\(4x+10 = 180\)

Step3: Solve for \(x\)

Subtract \(10\) from both sides:
\(4x=180 - 10\)
\(4x=170\)
Divide both sides by \(4\):
\(x=\frac{170}{4}=42.5\)

Step4: Find the measure of \(\angle3\)

Substitute \(x = 42.5\) into the expression for \(\angle3\):
\(\angle3=2x-10\)
\(\angle3=2\times42.5-10\)
\(\angle3=85 - 10\)
\(\angle3 = 75^{\circ}\)

Answer:

\(75\)