Elementary School Math Quiz: Add And Subtract Angle Measures

A clock face shows that the hour hand and minute hand form different angles with the 12 o'clock position. The hour hand makes a $90°$ angle with 12 o'clock, and the minute hand makes a $54°$ angle with 12 o'clock. Both hands are on the same side of 12 o'clock. What is the angle between the two hands?

Tommy draws an angle that measures $156°$. He then draws a ray inside this angle that creates two smaller angles. One of the smaller angles measures $89°$. If Tommy wants the other smaller angle to measure $75°$, by how many degrees is he off from his target?

A surveyor measures a large angle at a construction site. The angle measures $137°$ and is composed of four smaller, non-overlapping angles. Three of these angles measure $28°$, $35°$, and $41°$. What is the measure of the fourth angle?

Look at the angle diagram. A straight angle measuring $180°$ has been divided into three non-overlapping angles. Two of these angles measure $52°$ and $73°$. What equation could be used to find $x$, the measure of the third angle?

In the figure, ray $FH$ divides angle $EFG$ into two parts. The measure of angle $EFH$ is three times the measure of angle $HFG$. If angle $HFG$ measures $32°$, what is the measure of angle $EFG$?

Angle $XYZ$ is divided by two rays, $YA$ and $YB$, creating three separate angles. If angle $XYA = 29°$, angle $AYB = 41°$, and angle $BYZ = 35°$, what is the measure of angle $XYZ$?

Look at the diagram. Angle $ABC$ measures $84°$. Ray $BD$ is drawn so that angle $ABD$ measures $49°$. Ray $BD$ is inside angle $ABC$. What is the measure of angle $DBC$?

In the figure shown, angle $PQS$ has been divided into two parts by ray $QR$. The measure of angle $PQR$ is $67°$, and the measure of the entire angle $PQS$ is $115°$. What is the measure of angle $RQS$?

Look at the diagram. Ray $BC$ divides angle $ABD$ into two smaller angles. If angle $ABC$ measures $35°$ and angle $CBD$ measures $42°$, what is the measure of angle $ABD$?