Angles and Their Measure: Practice

First halve the whole to find $m\angle BOC=78^\circ$. Then halve that part.

$78^\circ \div 2 = 39^\circ$

Angle addition gives $8x+6=134$, so $8x=128$ and $x=16$.

$3(16)+8=56$

The other part is $5(16)-2=78$ degrees, so the smaller is $56^\circ$.

Set the parts equal: $7x-11=4x+16$. This gives $3x=27$, so $x=9$. Each part is $52^\circ$.

$52^\circ + 52^\circ = 104^\circ$

First find the other opening: $360^\circ-248^\circ=112^\circ$. Then bisect it.

$112^\circ \div 2 = 56^\circ$

The turn already made is $\frac7{12}\times360^\circ=210^\circ$.

$360^\circ - 210^\circ = 150^\circ$

Remove the final part from the straight opening to get $m\angle AOC=112^\circ$. The bisector splits that opening equally.

$112^\circ \div 2 = 56^\circ$

The selected zero gives a smaller opening of $138^\circ$. The reflex opening is the rest of the full turn.

$360^\circ - 138^\circ = 222^\circ$

Let the smaller part measure $x$ degrees. Then $x+(x+20)=170$, so $2x=150$ and $x=75$.

$75^\circ + 20^\circ = 95^\circ$

Equal measures give

$6t-4=2t+48.$

Subtract $2t$ and add 4 to get $4t=52$, so $t=13$. Each measure in degrees is

$6(13)-4=74.$

The measure is greater than zero and less than $90^\circ$, so both angles are acute.

Their sum gives $3a+6=123$, so $a=39$. The second part is $84^\circ$.

$84^\circ - 39^\circ = 45^\circ$

The bisector gives $m\angle AOP=143^\circ$. Subtract its known part.

$143^\circ - 61^\circ = 82^\circ$

Congruent angles are defined to have equal measures.

Exact equality establishes congruence; equal ray drawings, a shared point, or the same broad type does not.

Matching protractor readings alone give evidence limited by measurement precision.