Question

1. the measure of an angle is represented by ( 4x - 10^circ ). its angle bisector divides it into two equal parts, each measuring ( 35^circ ). what is the value of ( x )?
2. ( 7.5^circ )
3. ( 11.25^circ )
4. ( 18^circ )
5. ( 20^circ )

Explanation:

Step1: Understand the angle bisector property

The angle bisector divides the angle into two equal parts, so the original angle is twice the measure of each part. So the original angle \(4x - 10^\circ\) should equal \(2\times35^\circ\).
\[4x - 10^\circ=2\times35^\circ\]

Step2: Simplify the right - hand side

Calculate \(2\times35^\circ = 70^\circ\), so the equation becomes:
\[4x-10^\circ = 70^\circ\]

Step3: Solve for \(x\)

Add \(10^\circ\) to both sides of the equation:
\[4x=70^\circ + 10^\circ\]
\[4x=80^\circ\]
Then divide both sides by 4:
\[x=\frac{80^\circ}{4}\]
\[x = 20^\circ\]

Answer:

\(20^\circ\) (corresponding to the option with \(20^\circ\))