Math - How to find an angle of a line

and are parallel lines. Solve for .

Figure not drawn to scale.

Explanation

The angles are alternate exterior angles and are, therefore, equal.

$\small 6x-8=2x+20$

$\small 6x=2x+28$

$\small 4x=28$

$\small x=7$

Lines and are parallel. Which angle is congruent to angle ?

Parallel_lines

Explanation

When two lines are parallel, corresponding angles are congruent. Because we don't know if lines and are parallel, we can't make any conclusions about angles 2 and 3.

With the given information, we can ignore line , as it has no relation to angle . This leaves angles 1 and 4 as possible answers. Angle 4 will be congruent to angle , while angle 1 will supplement angle .

$\dpi{100} \small \overline{AB}$ is a straight line. $\dpi{100} \small \overline{CD}$ intersects $\dpi{100} \small \overline{AB}$ at point $\dpi{100} \small E$ . If $\dpi{100} \small \angle AEC$ measures 120 degrees, what must be the measure of $\dpi{100} \small \angle BEC$ ?

None of the other answers

$\dpi{100} \small 70$ degrees

$\dpi{100} \small 65$ degrees

$\dpi{100} \small 75$ degrees

$\dpi{100} \small 60$ degrees

Explanation

$\dpi{100} \small \angle AEC$ & $\dpi{100} \small \angle BEC$ must add up to 180 degrees. So, if $\dpi{100} \small \angle AEC$ is 120, $\dpi{100} \small \angle BEC$ (the supplementary angle) must equal 60, for a total of 180.

If $\angle A$ measures $(40-10x)^{\circ}$ , which of the following is equivalent to the measure of the supplement of $\angle A$ ?

$(10x+140)^{\circ}$

$(10x+50)^{\circ}$

$(50-10x)^{\circ}$

$(140-10x)^{\circ}$

$(100x)^{\circ}$

Explanation

When the measure of an angle is added to the measure of its supplement, the result is always 180 degrees. Put differently, two angles are said to be supplementary if the sum of their measures is 180 degrees. For example, two angles whose measures are 50 degrees and 130 degrees are supplementary, because the sum of 50 and 130 degrees is 180 degrees. We can thus write the following equation:

$\dpi{100} measure\ of\ \angle A+ measure\ of\ supplement\ of\ \angle A=180$

$\dpi{100} 40-10x+ measure\ of\ supplement\ of\ \angle A=180$

Subtract 40 from both sides.

$\dpi{100} -10x+ measure\ of\ supplement\ of\ \angle A=140$

Add $\dpi{100} 10x$ to both sides.

$\dpi{100} measure\ of\ supplement\ of\ \angle A=140+10x=10x+140$

The answer is $(10x+140)^{\circ}$ .

Lines $\small l$ and $\small m$ are parallel. Which of the following pairs of angles are supplementary?

$10\ \text{and}\ 13$

$9\ \text{and}\ 13$

$12\ \text{and}\ 8$

$12\ \text{and}\ 6$

Explanation

Coresponding angles can be found when a line crosses two parallel lines. Angles 10 and 14 are equal, because corresponding angles are equal. Angles 14 and 13 are supplementary because together they form a straight line. If angles 10 and 14 are equal, then angles 10 and 13 must be supplementary as well.

Parallellines

In the diagram, AB || CD. What is the value of a+b?

None of the other answers.

140°

80°

60°

160°

Explanation

Refer to the following diagram while reading the explanation:

Parallellines-answer

We know that angle b has to be equal to its vertical angle (the angle directly "across" the intersection). Therefore, it is 20°.

Furthermore, given the properties of parallel lines, we know that the supplementary angle to a must be 40°. Based on the rule for supplements, we know that a + 40° = 180°. Solving for a, we get a = 140°.

Therefore, a + b = 140° + 20° = 160°

In the following diagram, lines and are parallel to each other. What is the value for ?

Sat_math_166_03

It cannot be determined

Explanation

When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.

Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.

Angle

Give another name for $\angle AVC$ .

$\angle DVA$

$\angle ACV$

$\angle VAD$

$\angle V$

$\angle CVD$

Explanation

Since the angle is called $\angle AVC$ , it has vertex - the middle letter is always the vertex - and it is the union of rays $\overrightarrow{VA}$ and $\overrightarrow{VC}$ . Another name for $\overrightarrow{VC}$ is $\overrightarrow{VD}$ , since is also on that ray, so the angle can be said to be the union of $\overrightarrow{VA}$ and $\overrightarrow{VD}$ ; this makes $\angle DVA$ a valid name for the angle.

$\angle ACV$ and $\angle VAD$ are not valid, since the middle letter is not vertex . $\angle CVD$ is not valid, since and are on the same side of the angle. $\angle V$ is not valid; an angle can be named using only its vertex only if it is the only angle in the diagram with that vertex, and that is not the case here.

Angles

Figure not drawn to scale.

In the figure above, APB forms a straight line. If the measure of angle APC is eighty-one degrees larger than the measure of angle DPB, and the measures of angles CPD and DPB are equal, then what is the measure, in degrees, of angle CPB?

114

Explanation

Let x equal the measure of angle DPB. Because the measure of angle APC is eighty-one degrees larger than the measure of DPB, we can represent this angle's measure as x + 81. Also, because the measure of angle CPD is equal to the measure of angle DPB, we can represent the measure of CPD as x.

Since APB is a straight line, the sum of the measures of angles DPB, APC, and CPD must all equal 180; therefore, we can write the following equation to find x:

x + (x + 81) + x = 180

Simplify by collecting the x terms.

3x + 81 = 180

Subtract 81 from both sides.

3x = 99

Divide by 3.

x = 33.

This means that the measures of angles DPB and CPD are both equal to 33 degrees. The original question asks us to find the measure of angle CPB, which is equal to the sum of the measures of angles DPB and CPD.

measure of CPB = 33 + 33 = 66.

The answer is 66.

Two pairs of parallel lines intersect:

Screen_shot_2013-03-18_at_10.29.11_pm

If A = 135o, what is 2*|B-C| = ?

140°

150°

160°

170°

180°

Explanation

By properties of parallel lines A+B = 180o, B = 45o, C = A = 135o, so 2*|B-C| = 2* |45-135| = 180o

How to find an angle of a line

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