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. not drawn to scale

Explanation:

Step1: Set up the equation

Since $\angle ADC$ is a right - angle, $\angle ADB+\angle BDC = 90^{\circ}$. So, $(6x - 4)+(4x + 24)=90$.

Step2: Combine like terms

Combine the $x$ terms and the constant terms: $6x+4x-4 + 24=90$, which simplifies to $10x+20 = 90$.

Step3: Isolate the variable term

Subtract 20 from both sides of the equation: $10x+20-20=90 - 20$, resulting in $10x=70$.

Step4: Solve for x

Divide both sides of the equation by 10: $\frac{10x}{10}=\frac{70}{10}$, so $x = 7$.

Answer:

$x = 7$