Question

find the value of x
30°
find the degree of each angle.
(x + 3)°
(x - 1)°
(x + 1)°
find the value of x.
5x+7
3x+13
bisect ∠aop and ∠poq:
provide the degrees of each angle.
27°
find the measure of each angle.
(2x + 3)°
(x - 6)°
find the measure of each angle.
(x - 2)°
(5x + 4)°
(3x + 7)°

Explanation:

Step1: First problem - find x

The angle shown is a right - angle (90°). So, $x + 30=90$.
Solve for $x$: $x=90 - 30$.
$x = 60$.

Step2: Second problem - find angles

The sum of the angles around a point is 90°. So, $(x + 1)+(x - 1)+(x + 3)=90$.
Combine like - terms: $3x+3 = 90$.
Subtract 3 from both sides: $3x=90 - 3=87$.
Divide both sides by 3: $x=\frac{87}{3}=29$.
The angles are:
$(x + 1)=(29 + 1)=30°$, $(x - 1)=(29 - 1)=28°$, $(x + 3)=(29+3)=32°$.

Step3: Third problem - find x

The two angles are supplementary (sum to 180°). So, $(5x + 7)+(3x + 13)=180$.
Combine like - terms: $8x+20 = 180$.
Subtract 20 from both sides: $8x=180 - 20 = 160$.
Divide both sides by 8: $x=\frac{160}{8}=20$.

Step4: Fourth problem - find angles

The sum of the angles is 180°. So, $(5x + 4)+(3x + 7)+(x - 2)=180$.
Combine like - terms: $9x + 9=180$.
Subtract 9 from both sides: $9x=180 - 9 = 171$.
Divide both sides by 9: $x = 19$.
The angles are: $(5x + 4)=5\times19+4=95 + 4=99°$, $(3x + 7)=3\times19+7=57 + 7=64°$, $(x - 2)=19 - 2=17°$.

Step5: Bisecting angles

To bisect an angle means to divide it into two equal parts. But without angle measures for $\angle AOP$ and $\angle POQ$, we can't find the numerical values of the bisected angles. We can only state the general concept that if $\angle AOP=\alpha$ and $\angle POQ=\beta$, then the bisected angles of $\angle AOP$ will be $\frac{\alpha}{2}$ each and the bisected angles of $\angle POQ$ will be $\frac{\beta}{2}$ each.

Answer:

First problem: $x = 60$
Second problem: Angles are 30°, 28°, 32°
Third problem: $x = 20$
Fourth problem: Angles are 99°, 64°, 17°
Fifth problem: General concept of angle - bisection stated, no numerical values without given angle measures.