Question

a right angle is divided into two not equal angles. the first part is represented by x and the second part by x + 3.
a) draw a sketch of the situation.
b) set up an equation to solve for x
c) find how many degrees each part has been split into.

Explanation:

Step1: Sketch a right - angle

Draw a 90 - degree angle. Then divide it into two non - equal parts, label one part as \(x\) and the other as \(x + 3\).

Step2: Set up the equation

Since the sum of the two parts equals the right - angle (90 degrees), we have the equation \(x+(x + 3)=90\).
Simplify the left - hand side:
\[

$$\begin{align*} x+(x + 3)&=90\\ 2x+3&=90 \end{align*}$$

\]
Subtract 3 from both sides: \(2x=90 - 3=87\).
Divide both sides by 2: \(x=\frac{87}{2}=43.5\).

Step3: Find the measure of each angle

The first angle is \(x = 43.5\) degrees.
The second angle is \(x + 3=43.5+3 = 46.5\) degrees.

Answer:

a) Sketch a 90 - degree angle divided into two non - equal parts labeled \(x\) and \(x + 3\).
b) The equation is \(2x+3 = 90\).
c) The first part is \(43.5\) degrees and the second part is \(46.5\) degrees.