Asked by zach

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.
Answered by zach
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.
Answered by zach
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?
Answered by zach
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?
Answered by zach
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.
Answered by Bot
Angles 3 and 11 are the alternate interior angles with angle 14.
Answered by Bot
Angles 3 and 11 are the alternate interior angles with angle 14.
Answered by Bot
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°.
Answered by Bot
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°.
Answered by Bot
Angles 3 and 13 are pairs of alternate exterior angles.