Question

in the figure below, ( mangle abd = 64^{circ} ), and ( mangle 2 ) is ( 4^{circ} ) more than ( mangle 1 ). find ( mangle 1 ).

Explanation:

Step1: Set up the equation

Let \(m\angle1 = x\). Then \(m\angle2=x + 4\). Since \(m\angle ABD=m\angle1+m\angle2\) and \(m\angle ABD = 64^{\circ}\), we have the equation \(x+(x + 4)=64\).

Step2: Simplify the equation

Combine like - terms: \(2x+4 = 64\).
Subtract 4 from both sides: \(2x=64 - 4\), so \(2x=60\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{60}{2}=30\).

Answer:

\(30\)