Question

Draw an angle and then draw the opposite ray to one of its sides, to form a linear pair. Find the measure of the angle formed by the angle bisector of the original angle and the opposite ray if the original angle measures 50°, 90°, and 150°. 1. If the angle equals 50°, then the measurement of the required angle is ? 2. If the angle equals 90°, then the measurement of the required angle is ? 3. If the angle equals 150°, then the measurement of the required angle is ?

Answer 1

Answer:

(1)155 degrees

(2)135 degrees

(3)105 degrees

Step-by-step explanation:

Let the original angle $= \theta$

Angle Bisector of the original angle = $\dfrac{ \theta}{2}$

If the other angle forms a linear pair, then:

The other angle, $\beta=180^\circ-\theta$

Therefore, the measure of the angle formed by the angle bisector of the original angle and the opposite ray is:

$\dfrac{ \theta}{2}+180^\circ-\theta\\=180^\circ-\dfrac{ \theta}{2}$

(1)If the angle equals 50°

Then the measurement of the required angle

$=180^\circ-\dfrac{ 50}{2}\\=180^\circ-25^\circ\\=155^\circ$

(2)If the angle equals 90°

Then the measurement of the required angle

$=180^\circ-\dfrac{ 90}{2}\\=180^\circ-45^\circ\\=135^\circ$

{3)If the angle equals 150°

Then the measurement of the required angle

$=180^\circ-\dfrac{ 150}{2}\\=180^\circ-75^\circ\\=105^\circ$

See attachment for an example of the graphical solution.