Question

refer to the figure.
if ( mangle adb=(6x - 4)^{circ} ) and ( mangle bdc=(4x + 24)^{circ} ), find the value of ( x ) such that ( angle adc ) is a right angle.
( x= )

Explanation:

Step1: Use the angle - addition postulate

Since \(\angle ADC=\angle ADB+\angle BDC\) and \(\angle ADC = 90^{\circ}\) (right - angle), we have the equation \((6x - 4)+(4x + 24)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(6x-4 + 4x+24=(6x + 4x)+(-4 + 24)=10x+20\). So the equation becomes \(10x+20 = 90\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(10x+20-20=90 - 20\), which gives \(10x=70\). Then divide both sides by 10: \(x=\frac{70}{10}=7\).

Answer:

\(7\)