QUESTION 1
The angle [tex]33x+3[/tex] and [tex]135\degree[/tex] are alternate exterior angles.
Since alternate interior angles are congruent, we must have;
[tex]33x+3=135\degree[/tex]
Group similar terms.
[tex]\Rightarrow 33x=135-3[/tex]
[tex]\Rightarrow 33x=132[/tex]
QUESTION 10
We solve the following equation for the two alternate exterior angles to find x.
[tex]x+134=130[/tex]
[tex]\Rightarrow x=130-134[/tex]
[tex]\Rightarrow x=-4[/tex]
[tex]\Rightarrow x=\frac{132}{33}[/tex]
[tex]\Rightarrow x=4[/tex].
QUESTION 2
The angle [tex]120\degree[/tex] and [tex]31x-4[/tex] degree angle are alternate interior angles.
Alternate interior angles are also equal
[tex]\Rightarrow 31x-4=120\degree[/tex]
[tex]\Rightarrow 31x=120+4[/tex]
[tex]\Rightarrow 31x=124[/tex]
[tex]\Rightarrow x=\frac{124}{31}[/tex]
[tex]\Rightarrow x=4[/tex]
QUESTION 3
The angle [tex]120\degree[/tex] and [tex]x+124[/tex] degree angle are alternate interior angles.
Alternate interior angles are congruent
[tex]\Rightarrow x+124=120\degree[/tex]
[tex]\Rightarrow x=120-124[/tex]
[tex]\Rightarrow x=-4[/tex]
QUESTION 4
The given angles, [tex]40x+5[/tex] and [tex]42x-1[/tex] are alternate interior angles.
[tex]\Rightarrow 40x+5=42x-1[/tex]
Group like terms;
[tex]\Rightarrow 5+1=42x-40x[/tex]
[tex]\Rightarrow 6=2x[/tex]
Divide both sides by 2 to get;
[tex]\Rightarrow x=3[/tex]
QUESTION 5
The given angles, [tex]20x+4[/tex] and [tex]19x+9[/tex] are alternate interior angles.
[tex]\Rightarrow 20x+4=19x+9[/tex]
Group like terms;
[tex]\Rightarrow 20x-19x=9-4[/tex]
[tex]\Rightarrow x=5[/tex]
QUESTION 6
The given angles, [tex]11x[/tex] and [tex]-9+12x[/tex] are alternate exterior angles.
Since the alternate exterior angles are congruent, we have;
[tex]-9+12x=11x[/tex]
We group similar terms to obtain;
[tex]12x-11x=9[/tex]
[tex]\Rightarrow x=9[/tex]
QUESTION 7
The two angles, [tex]x+88[/tex] and [tex]80[/tex].
The two alternate interior angles are congruent.
[tex]\Rightarrow x+88=80\degree[/tex]
[tex]\Rightarrow x=80-88[/tex]
[tex]\Rightarrow x=-8[/tex]
QUESTION 9
The two angle alternate interior angles.
These angles are congruent.
This implies that;
[tex]x+75=70[/tex]
[tex]\Rightarrow x=70-75[/tex]
[tex]\Rightarrow x=-5[/tex]
QUESTION 10
We solve the following equation for the two alternate exterior angles.
[tex]x+134=130[/tex]
[tex]\Rightarrow x=130-134[/tex]
[tex]\Rightarrow x=-4[/tex]
