Which angle must be complementary to angle 3?
3 lines intersect to form 6 angles. Clockwise, from top left, the angles 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3.
Angle 6 must be complementary to angle 3, as they both add up to 90 degrees.
Which statement is true about angles 3 and 6?
3 lines intersect to form 6 angles. Clockwise, from top left, the angles 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3.
They are adjacent angles.
They are complementary angles.
They are supplementary angles.
They are vertical angles.
Angles 3 and 6 are complementary angles, because they add up to 90 degrees.
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1, 2 (90 degrees), 3, 4, 5, 6.
We are given that angle 4 has a measure of 11x degrees and angle 3 has a measure of 4x degrees. We know that the six angles formed by the intersection of three lines will add up to 360 degrees, so we can use this information to set up an equation:
Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 = 360
Since Angle 2 is a right angle with a measure of 90 degrees, we can substitute this value into the equation:
Angle 1 + 90 + 4x + 11x + Angle 5 + Angle 6 = 360
Simplifying the equation, we get:
Angle 1 + 15x + Angle 5 + Angle 6 = 270
We also know that angles 3 and 4 are adjacent angles, meaning they share a common vertex and a common side. Adjacent angles add up to the measure of the straight angle, which is 180 degrees. Using this information, we can set up another equation:
Angle 3 + Angle 4 = 180
Substituting the given measures for angles 3 and 4, we get:
4x + 11x = 180
Simplifying and solving for x, we get:
15x = 180
x = 12
Now that we know the value of x, we can find the measure of angle 3:
Angle 3 = 4x
Angle 3 = 4(12)
Angle 3 = 48 degrees
Therefore, the measure of angle 3 is 48 degrees.
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We know that angle 4 has a measure of 11x degrees and angle 3 has a measure of 4x degrees. We also know that angles 3 and 4 are adjacent angles, which means they share a common side. Adjacent angles add up to 180 degrees. Therefore, we can set up an equation:
4x + 11x = 180
Simplifying and solving for x, we get:
15x = 180
x = 12
Now that we know the value of x, we can find the measure of angle 3:
Angle 3 = 4x
Angle 3 = 4(12)
Angle 3 = 48 degrees
Therefore, the measure of angle 3 is 48 degrees.