When two lines are parallel, corresponding angles are congruent. Because we don't know if linesandare 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.

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.

Let x equal the measure of angle ABC, let y equal the measure of the supplement of angle ABC, and let z equal the measure of the complement of angle ABC.

Because x and y are supplements, the sum of their measures must equal 180. In other words, x + y = 180.

We are told that one-half of the measure of the supplement is equal to twice the measure of ABC. We could write this equation as follows:

(1/2)y = 2x.

Because x + y = 180, we can solve for y in terms of x by subtracting x from both sides. In other words, y = 180 – x. Next, we can substitute this value into the equation (1/2)y = 2x and then solve for x.

(1/2)(180-x) = 2x.

Multiply both sides by 2 to get rid of the fraction.

(180 – x) = 4x.

Add x to both sides.

180 = 5x.

Divide both sides by 5.

x = 36.

The measure of angle ABC is 36 degrees. However, the original question asks us to find the measure of the complement of ABC, which we denoted previously as z. Because the sum of the measure of an angle and the measure of its complement equals 90, we can write the following equation:

x + z = 90.

Now, we can substitute 36 as the value of x and then solve for z.

36 + z = 90.

Subtract 36 from both sides.

z = 54.

The answer is 54.

Refer to the following diagram while reading the explanation:

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°

Intersecting lines create two pairs of vertical angles which are congruent. Therefore, we can deduce thaty= measure of angleAED.

Furthermore, intersecting lines create adjacent angles that are supplementary (sum to 180 degrees). Therefore, we can deduce thatx+y+z+ (measure of angleAED) = 360.

Substituting the first equation into the second equation, we get

x+ (measure of angleAED) +z+ (measure of angleAED) = 360

2(measure of angleAED) +x+z= 360

2(measure of angleAED) = 360 – (x+z)

Divide by two and get:

measure of angleAED= 180 – 1/2(x+z)

Since the angle is called,它有顶点- the middle letter isalwaysthe vertex - and it is the union of raysand. Another name foris, sinceis also on that ray, so the angle can be said to be the union ofand; this makesa valid name for the angle.

andare not valid, since the middle letter is not vertex.is not valid, sinceandare on the same side of the angle.is not valid; an angle can be named using only its vertex only if it is theonlyangle in the diagram with that vertex, and that is not the case here.

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.

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

Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:

Since we know opposite angles are equal, it follows that angleand.

Imagine a parallel line passing through point. The imaginary line would make opposite angles with&, the sum of which would equal. Therefore,.