In the diagram, the measure of angle 3 is 89°, and the measure of angle 6 is 88°.
A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 4?
Since angle 3 is 89° and angles 3 and 4 are supplementary, we know that angle 4 is 180° - 89° = 91°. Therefore, the measure of angle 4 is 91°.
In the diagram, what is the measure of angle 1 to the nearest degree?
A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are blank, 88 degrees, blank, (7 x + 4) degrees; blank, blank, (7 x minus 2) degrees, 1.
Since angles 1 and 2 are supplementary and angle 2 has a measure of 88 degrees, we know that angle 1 has a measure of 180 degrees - 88 degrees = 92 degrees. Therefore, the measure of angle 1 to the nearest degree is 92 degrees.
In the diagram, which pair of angles are vertical angles?
A transversal intersects 2 lines to form 8 angles. Clockwise from the top, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
Vertical angles are formed when two lines intersect, and they are opposite to each other. In the given diagram, vertical angles are angles that are opposite to each other across the intersection of the two lines.
So, the pair of angles that are vertical angles are:
- Angle 2 and angle 7: They are opposite to each other across the intersection of the two lines, and they have the same measure of 88 degrees.
Therefore, the pair of angles that are vertical angles are angle 2 and angle 7.
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In the given diagram, the pair of angles that are vertical angles are angles:
- 1 and 5: They are opposite to each other across the intersection of the two lines.
Vertical angles are always congruent, meaning they have the same measure. Therefore, angle 1 is congruent to angle 5, and they are vertical angles.
In the diagram, the measure of angle 5 is (10x – 9)°, and the measure of angle 7 is (9x)°. What is the measure of angle 6, to the nearest degree?
A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 6, to the nearest degree?
Since angle 5 and angle 6 are supplementary, we know that:
angle 5 + angle 6 = 180 degrees
Substituting the given measure of angle 5, we get:
(10x - 9) + angle 6 = 180
Simplifying the equation, we get:
angle 6 = 180 - (10x - 9)
angle 6 = 189 - 10x
Similarly, since angle 6 and angle 7 are supplementary, we know that:
angle 6 + angle 7 = 180 degrees
Substituting the given measure of angle 7, we get:
angle 6 + (9x) = 180
Simplifying the equation, we get:
angle 6 = 180 - (9x)
Now we can set these two expressions for angle 6 equal to each other and solve for x:
189 - 10x = 180 - 9x
Simplifying the equation, we get:
x = 9
Now we can substitute the value of x back into one of the expressions for angle 6 and simplify:
angle 6 = 180 - (9x)
angle 6 = 180 - (9*9)
angle 6 = 99
Therefore, the measure of angle 6 is about 99 degrees to the nearest degree.
In the diagram, how many angles are alternate exterior angles with angle 16?
4 lines intersect to form 16 angles. The angles created, clockwise from top left are 1, 2, 3, 4; 5, 6, 7, 8; 13, 14, 15, 16; 9, 10, 11, 12.