Question

find the measure of each angle.
12x + 5
8x + 5
12x + 5 = \square^\circ
8x + 5 = \square^\circ
(simplify your answers. type an integer or a fraction.)

Explanation:

Step1: Set up the equation

The two angles \(12x + 5\) and \(8x + 5\) form a right angle (since there is a right - angle symbol), so their sum is \(90^\circ\).
We can write the equation: \((12x + 5)+(8x + 5)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(12x+8x + 5 + 5=90\)
\(20x+10 = 90\)

Step3: Solve for \(x\)

Subtract 10 from both sides: \(20x=90 - 10\)
\(20x = 80\)
Divide both sides by 20: \(x=\frac{80}{20}=4\)

Step4: Find the measure of \(12x + 5\)

Substitute \(x = 4\) into \(12x+5\): \(12\times4+5=48 + 5=53\)

Step5: Find the measure of \(8x + 5\)

Substitute \(x = 4\) into \(8x+5\): \(8\times4+5=32 + 5=37\)

Answer:

For \(12x + 5\): \(53^\circ\)
For \(8x + 5\): \(37^\circ\)