Question

30 POINTS For Answers To Questions 1-10

Answer 1

QUESTION 1

The angle $33x+3$ and $135\degree$ are alternate exterior angles.

Since alternate interior angles are congruent, we must have;

$33x+3=135\degree$

Group similar terms.

$\Rightarrow 33x=135-3$

$\Rightarrow 33x=132$

QUESTION 10

We solve the following equation for the two alternate exterior angles to find x.

$x+134=130$

$\Rightarrow x=130-134$

$\Rightarrow x=-4$

$\Rightarrow x=\frac{132}{33}$

$\Rightarrow x=4$.

QUESTION 2

The angle $120\degree$ and $31x-4$ degree angle are alternate interior angles.

Alternate interior angles are also equal

$\Rightarrow 31x-4=120\degree$

$\Rightarrow 31x=120+4$

$\Rightarrow 31x=124$

$\Rightarrow x=\frac{124}{31}$

$\Rightarrow x=4$

QUESTION 3

The angle $120\degree$ and $x+124$ degree angle are alternate interior angles.

Alternate interior angles are congruent

$\Rightarrow x+124=120\degree$

$\Rightarrow x=120-124$

$\Rightarrow x=-4$

QUESTION 4

The given angles, $40x+5$ and $42x-1$ are alternate interior angles.

$\Rightarrow 40x+5=42x-1$

Group like terms;

$\Rightarrow 5+1=42x-40x$

$\Rightarrow 6=2x$

Divide both sides by 2 to get;

$\Rightarrow x=3$

QUESTION 5

The given angles, $20x+4$ and $19x+9$ are alternate interior angles.

$\Rightarrow 20x+4=19x+9$

Group like terms;

$\Rightarrow 20x-19x=9-4$

$\Rightarrow x=5$

QUESTION 6

The given angles, $11x$ and $-9+12x$ are alternate exterior angles.

Since the alternate exterior angles are congruent, we have;

$-9+12x=11x$

We group similar terms to obtain;

$12x-11x=9$

$\Rightarrow x=9$

QUESTION 7

The two angles, $x+88$ and $80$.

The two alternate interior angles are congruent.

$\Rightarrow x+88=80\degree$

$\Rightarrow x=80-88$

$\Rightarrow x=-8$

QUESTION 9

The two angle alternate interior angles.

These angles are congruent.

This implies that;

$x+75=70$

$\Rightarrow x=70-75$

$\Rightarrow x=-5$

QUESTION 10

We solve the following equation for the two alternate exterior angles.

$x+134=130$

$\Rightarrow x=130-134$

$\Rightarrow x=-4$