Lines and Angles: questions with answers

Point Y lies between D and F. So the line segments DY and YF together make the whole line segment DF. Their lengths add up: DY + YF = DF.

$\overrightarrow{RS}$ starts at R and goes through S. $\overrightarrow{SR}$ starts at S and goes through R. Since the starting points and directions are different, they do not name the same ray.

The angle is the amount of rotation about vertex P from ray PA to ray PB. The marked turn is 45°.

Angle size depends on the amount of turn about the hinge, not on the physical size of the object or the gap at the far ends. The right opening has a turn of 110°, which is greater than 90°.

A horizontal line and a vertical line meet at right angles. So the marked angle is a right angle, and the two lines are perpendicular.

Each right angle is 90°. The combined angle is 90° + 90° = 180°. An angle of 180° is a straight angle.

A right angle is half of a straight angle. Half of $180^\circ$ is $90^\circ$, so a right angle measures $90^\circ$.

A straight angle is half of a full turn. Half of $360^\circ$ is $180^\circ$, so a straight angle measures $180^\circ$.

The point P is only a guide point for the required measure. To complete the construction, draw ray OP from the vertex O through P. The angle is then formed by rays OA and OP.

The dot D records the direction for 90°, but an angle needs two rays with the same endpoint. The construction is unfinished because ray BD from B through D has not been drawn.

Angle ABC and angle CBD are adjacent angles. They have the common arm BC, but they do not overlap. Sharing an arm is not the same as sharing a part of the opening, so nothing is counted twice. Together the two angles make angle ABD. So measure of angle ABD = measure of angle ABC + measure of angle CBD.

The angle does not start at 0 degrees on the protractor scale. Its measure is the difference between the two readings: 110 degrees - 50 degrees = 60 degrees.

The equal marks show that $\angle WAZ$ is divided into three equal parts. The trisectors are the internal rays that make those three equal parts, so the trisectors are $AX$ and $AY$.

Trisectors are the internal rays that divide the whole angle into three equal parts. The equal angles are made by rays $AP$, $AQ$, $AR$, and $AS$, so the internal trisector rays are $AQ$ and $AR$. The extra ray $AT$ is not a trisector because it is not one of the rays forming the three marked equal parts.

A point is in the interior of angle 2 only if it lies in the region between the two arms of angle 2. Point B is in that region. Point C is in that region. The answer is: Both B and C.