In the diagram, which two angles are alternate interior angles with angle 14?
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.
Angles 3 and 11 are the alternate interior angles with angle 14.
In the diagram, which two angles are alternate interior angles with angle 14?
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.
Angles 3 and 11 are the alternate interior angles with angle 14.
In the diagram, the measure of angle 6 is 98°.
A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 7?
If angles 5 and 6 are alternate interior angles, then they are congruent. Thus, angle 5 is also 98°.
Angles 6 and 7 are corresponding angles, which means they are congruent. Therefore, angle 7 is also 98°.
In the diagram, the measure of angle 2 is 126°, the measure of angle 4 is (7x)°, and the measure of angle 5 is (4x + 4)°.
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 7, to the nearest degree?
Angles 2 and 7 are corresponding angles, which means they are congruent. Therefore, angle 7 also measures 126°.
Angles 4 and 6 are alternate interior angles, which means they are congruent. Thus, 7x = angle 4 = angle 6.
Angles 5 and 3 are alternate interior angles, which means they are congruent. Thus,
4x + 4 = angle 5 = angle 3.
Since angles 3, 4, 6, and 8 form a straight line,
angle 3 + angle 4 + angle 6 + angle 8 = 360°.
Substituting the given values, we get:
126° + (7x)° + (7x)° + angle 8 = 360°
Simplifying the equation, we get:
14x + angle 8 = 234°
Now substituting 4x+4 for angle 5,
126° + (7x)° + (7x)° + 4x+4 + angle 8 = 360°
Simplifying we get:
18x + angle 8 = 230°
Solving for angle 8, we get:
angle 8 = 230° - 18x
Substituting this value into the previous equation, we get:
14x + (230° - 18x) = 234°
Simplifying this equation we get:
-4x = 4°
x = -1°.
Although x is negative, the absolute value of x will be positive.
Substituting x = 1° into the expression for angle 7, we get:
angle 7 = 126° (same as angle 2).
Therefore, the measure of angle 7 is approximately 126°.
Which angles are pairs of alternate exterior angles? Check all that apply.
4 lines intersect to form 16 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 9; 9, 10, 11, 12; 13, 14, 15, 16.
Angles 3 and 13 are pairs of alternate exterior angles.
To determine which two angles are alternate interior angles with angle 14 in the given diagram, we need to understand the concept of alternate interior angles.
Alternate interior angles are a pair of angles that are on the opposite sides of a transversal cutting through two parallel lines. They are located in the interior of the two parallel lines and are congruent (equal).
In the diagram, the angles created by the intersecting lines are labeled from 1 to 16. To find the alternate interior angles with angle 14, we need to identify another angle that:
- Is on the opposite side of a transversal
- Lies between the two parallel lines
- Is congruent to angle 14
Based on the given information, angles 14, 10, 11, and 15 are the angles located between the two parallel lines. We need to identify the angle that is congruent to angle 14.
Now, to find the alternate interior angle with angle 14, we need to look for the angle that is on the opposite side of the transversal (the line that intersects the other lines) and is in the interior of the two parallel lines.
From the diagram, we can see that angle 8 is on the opposite side of the transversal, and it also lies between the two parallel lines. Therefore, angle 8 is the alternate interior angle with angle 14.
Therefore, the two angles that are alternate interior angles with angle 14 in the given diagram are angle 14 and angle 8.