An illustration shows a horizontal line intersecting two parallel slanting lines. The angles the horizontal line forms with left parallel line are 1, 2, 3, and 4. Angles 1 and 2 are complementary. Angles 2 and 4 are complementary. Angles 4 and 3 are complementary. Angles 3 and 1 are complementary. Angles 1 and 4 are opposite each other. Angles 2 and 3 are opposite each other. The angles the horizontal line forms with right parallel line are 5, 6, 7, and 8. . Angles 5 and 6 are complementary. Angles 6 and 8 are complementary. Angles 8 and 7 are complementary. Angles 7 and 5 are complementary. Angles 5 and 8 are opposite each other. Angles 6 and 7 are opposite each other.
Which angle is a vertical angle with ∠5 ?
Angle 6 is a vertical angle with angle 5.
An illustration shows five rays emerging from a point labeled A, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.
If m∠2=47° , what is m∠4 ?
Since angles 1 and 2 form a right angle, and angle 2 is 47°, angle 1 must be 90° - 47° = 43°.
Therefore, angle 4 is vertical with angle 1 and must also be 43°.
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An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?
From the given angle measures, we can see that angles 5 and 8 are supplementary (they form a straight line), which means their measures add up to 180°.
So, we can write the equation as:
m∠5 + m∠8 = 180°
112 + (2x + 8) = 180
Solving for x:
2x + 120 = 180
2x = 60
x = 30
Therefore, x = 30.
For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?
Vertical angles are always congruent, meaning that they have the same measure. Therefore, we can set the measures of angles 1 and 3 equal to each other and solve for x:
m∠1 = m∠3
2x + 26 = 3x + 32
26 - 32 = 3x - 2x
-6 = x
Now that we have found the value of x, we can substitute it back into either equation to find the measure of each angle:
m∠1 = 2(-6) + 26 = -12 + 26 = 14°
m∠3 = 3(-6) + 32 = -18 + 32 = 14°
Therefore, both angles 1 and 3 have a measure of 14° each.
In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C . If m∠A=22° , write an equation that you can use to solve for m∠C
Since angle B is complementary to angle C, it means that the sum of angle B and angle C equals 90 degrees.
Given that angle A and angle B are vertical angles, they are congruent. So, if angle A has a measure of 22 degrees, then angle B also has a measure of 22 degrees.
Therefore, we can set up the equation:
m∠B + m∠C = 90
Substitute the known values:
22 + m∠C = 90
This is the equation that can be used to solve for the measure of angle C.