Angles and Their Measure: Practice

Use the scale starting at zero on the baseline ray. That is the inner scale, whose reading is $72^\circ$.

The smaller opening and the reflex opening fill one full turn.

$360^\circ - 118^\circ = 242^\circ$

Multiply the full turn by the fraction.

$\frac38 \times 360^\circ = 135^\circ$

This is between $90^\circ$ and $180^\circ$, so it is obtuse.

The two parts fill the whole, so subtract the known part.

$142^\circ - 59^\circ = 83^\circ$

The three parts add to the straight angle's $180^\circ$. The known parts total $103^\circ$.

$180^\circ - 103^\circ = 77^\circ$

The given measure is one of two equal parts. Add both parts to get the whole.

$43^\circ + 43^\circ = 86^\circ$

The two parts have equal measures.

$5x+6=8x-15$

Subtract $5x$ and add 15 to get $21=3x$. Divide by 3 to obtain

$x=\frac{21}{3}=7.$

A right angle measures $90^\circ$.

$5x+10=90$

Subtract 10 and divide by 5 to obtain $x=16$.

Angle addition needs the parts to fill the selected opening exactly once. A shared vertex alone does not guarantee that arrangement.

Choose a scale by its zero, not by whether it is inner or outer. Start at the zero on the leftward baseline and mark 137 on that same scale.

Halve the selected opening.

$206^\circ \div 2 = 103^\circ$

Each part is greater than $90^\circ$ and less than $180^\circ$, so it is obtuse.

A zero turn does not rotate the ray. A full turn rotates it all the way around, returning to the same direction after $360^\circ$.