To find the measure of angle D, we need to set up an equation using the given information.
From the illustration, we know that angle A is labeled as (4x - 10)°. Angle D is labeled as (2x + 22)°.
Since angle D is opposite to angle A and they are formed by intersecting lines, we can say that angle A and angle D are supplementary angles.
Supplementary angles add up to 180°.
So, we have the equation:
(4x - 10)° + (2x + 22)° = 180°
Simplifying the equation, we get:
6x + 12° = 180°
Subtracting 12° from both sides of the equation, we get:
6x = 168°
Divide both sides of the equation by 6, we get:
x = 28°
Now, we can substitute the value of x into the expression for angle D:
(2x + 22)° = (2(28) + 22)° = (56 + 22)° = 78°
Therefore, the measure of angle D is 78°.
se the image to answer the question.
An illustration shows intersecting lines and rays. The resulting angles are labeled. A vertical line is intersected by an upward slanting line from left to right. A downward slanting ray extends from the point where the lines intersect to the bottom right. Starting from the top part of the vertical line, the first angle betwee the vertical line and the slanting line is labeled A. Moving clockwise, next angle is labeled Angle B, then Angle C, then Angle D, and then Angle E. All of the angles have degree signs next to their labels, but they do not have degree measurements.
In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?
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From the given information, we know that angle D is labeled as (2x + 22)°.
To find the measure of angle D, we need to set up an equation using the given information.
Since angle D is opposite to angle A and they are formed by intersecting lines, we can say that angle A and angle D are vertical angles.
Vertical angles are congruent, meaning they have the same measure. So, we can set up the equation:
m∠A = m∠D
Substituting the values, we have:
(4x - 10)° = (2x + 22)°
Now, we can solve for x.
4x - 10 = 2x + 22
Subtracting 2x from both sides, we get:
2x - 10 = 22
Adding 10 to both sides, we get:
2x = 32
Dividing both sides by 2, we get:
x = 16
Now, we can substitute the value of x into the expression for angle D:
(2x + 22)° = (2(16) + 22)° = (32 + 22)° = 54°
Therefore, the measure of angle D is 54°.
From the given information, we know that angle D is labeled as (2x + 22)°.
To find the measure of angle D, we need to set up an equation using the given information.
Since angle D is opposite to angle A and they are formed by intersecting lines, we can say that angle A and angle D are vertical angles.
Vertical angles are congruent, meaning they have the same measure. So, we can set up the equation:
m∠A = m∠D
Substituting the values, we have:
(4x - 10)° = (2x + 22)°
Now, we can solve for x.
4x - 10 = 2x + 22
Subtracting 2x from both sides, we get:
2x - 10 = 22
Adding 10 to both sides, we get:
2x = 32
Dividing both sides by 2, we get:
x = 16
Now, we can substitute the value of x into the expression for angle D:
(2x + 22)° = (2(16) + 22)° = (32 + 22)° = 54°
Therefore, the measure of angle D is 54°.