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.
6 degrees
24 degrees
66 degrees
90 degrees
The answer is 66 degrees.
We know that angle 4 is 11 times angle 1, so we can set up the equation:
angle 4 = 11x
We also know that angle 2 is 90 degrees, so we can set up another equation:
angle 1 + angle 2 + angle 3 = 180 degrees
Substituting angle 4 for 11x, we get:
angle 1 + 90 degrees + angle 3 + 11x = 180 degrees
Simplifying:
angle 1 + angle 3 + 11x = 90 degrees
We also know that angle 3 is 4 times angle 1, so we can substitute that in:
angle 1 + 4x + 11x = 90 degrees
Simplifying:
15x + angle 1 = 90 degrees
We don't know the exact measure of angle 1, but we don't need to. We just need to solve for x:
15x = 90 degrees - angle 1
Now we can plug in the answer choices for angle 1 and see which one gives us an integer value for x:
- If angle 1 is 6 degrees, then 15x = 84 degrees and x = 5.6 degrees (not an integer)
- If angle 1 is 24 degrees, then 15x = 66 degrees and x = 4.4 degrees (not an integer)
- If angle 1 is 66 degrees, then 15x = 24 degrees and x = 1.6 degrees (an integer!)
Therefore, the measure of angle 3 is:
angle 3 = 4x = 4(1.6) = 6.4 degrees ≈ 66 degrees (rounded to the nearest whole number)
If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angle 2 in degrees?
A horizontal line. A line extends from the line to form a 90 degree angle. Another line cuts through the 2 lines to form angles 1 and 2, which total 90 degrees.
32 degrees
38 degrees
58 degrees
66 degrees
The answer is 38 degrees.
We know that angles 1 and 2 add up to 90 degrees, so we can set up the equation:
angle 1 + angle 2 = 90 degrees
We also know that angle 1 is (3x - 4) degrees and angle 2 is (4x + 10) degrees, so we can substitute those into the equation:
(3x - 4) + (4x + 10) = 90
Simplifying:
7x + 6 = 90
Subtracting 6 from both sides:
7x = 84
Dividing both sides by 7:
x = 12
Now we can plug in x = 12 to find the measure of angle 2:
angle 2 = 4x + 10 = 4(12) + 10 = 58 degrees
Therefore, the measure of angle 2 is 58 degrees.
If the measure of Angle B E C is (2 x + 3) degrees and x = 30, which expression could represent the measure of Angle A E D?
Lines A C and B D intersect at point E.
(4 x minus 3) degrees
(3 x minus 27) degrees
(5 x minus 33) degrees
(x + 43) degrees
We can begin by finding the measure of angle BEC using the given value of x:
angle BEC = 2x + 3 = 2(30) + 3 = 63 degrees
We know that angles AED and BEC are supplementary, meaning they add up to 180 degrees. So we can set up the equation:
angle AED + angle BEC = 180 degrees
Substituting 63 degrees for angle BEC, we get:
angle AED + 63 degrees = 180 degrees
Simplifying:
angle AED = 117 degrees
Now we can plug in x = 30 to the answer choices and see which one gives us 117 degrees:
- If the expression is 4x - 3, then angle AED = 4(30) - 3 = 117 degrees (matches our answer)
- If the expression is 3x - 27, then angle AED = 3(30) - 27 = 33 degrees (not a match)
- If the expression is 5x - 33, then angle AED = 5(30) - 33 = 117 degrees (matches our answer)
- If the expression is x + 43, then angle AED = 30 + 43 = 73 degrees (not a match)
Therefore, the expressions that could represent the measure of angle AED are 4x - 3 and 5x - 33.
Which is a correct name for the angle shown?
Line segments A B and B C combine to form an angle.
Angle A
Angle C
Angle A C B
Angle C B A
A correct name for the angle shown is "Angle ACB". This is because angles are named using three points, with the vertex point listed in the middle. In this case, the vertex of the angle is point B, and the two rays of the angle are AB and BC. Therefore, the angle is named ACB, with the vertex letter listed in the middle.
If the measure of Angle F G H is 64 degrees and the measure of Angle E G D is (4 x + 8) degrees, what is the value of x?
We cannot determine the value of x without more information. The given values do not appear to have any direct relationship that would allow us to set up an equation and solve for x.
It is possible that there is some additional information about the angles or their relationships that was not included in the problem statement. Without that information, we cannot determine the value of x.
If the measure of Angle F G H is 64 degrees and the measure of Angle E G D is (4 x + 8) degrees, what is the value of x?
Lines E H and D F intersect at point G.
Since lines EH and DF intersect at point G, we know that angles FGH and EGD are vertical angles and are therefore congruent. In other words, we can set up the equation:
angle FGH = angle EGD
Substituting the given values:
64 degrees = 4x + 8
Solving for x:
56 degrees = 4x
x = 14
Therefore, the value of x is 14.
If the measure of angle 2 is 92 degrees and the measure of angle 4 is (one-half x) degrees, what is the value of x?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 4, 3, 2.
Since angles 2 and 4 are opposite each other and are therefore congruent, we can set up the equation:
angle 2 = angle 4
Substituting the given values:
92 degrees = 0.5x
Solving for x:
x = 184
Therefore, the value of x is 184 degrees.
What is another name for Angle 1?
Line segments H E and E F combine to form an angle. Line segment E G comes out of the angle to form 2 angles. Angle H E G is 2 and angle G E F is 1.
Angle 1 can also be referred to as angle FEG. This is because angles are typically named using three letters, with the middle letter being the vertex of the angle. The rays that form the angle are listed in the order in which they appear when moving counterclockwise around the vertex. In this case, the rays that form angle 1 are EF and EG, so the angle can also be referred to as angle FEG.
If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angle 2 in degrees?
A horizontal line. A line extends from the line to form a 90 degree angle. Another line cuts through the 2 lines to form angles 1 and 2, which total 90 degrees.
We can begin solving the problem by using the fact that angles 1 and 2 add up to 90 degrees:
angle 1 + angle 2 = 90 degrees
We also know that angle 2 is (4x + 10) degrees and angle 1 is (3x - 4) degrees, so we can substitute those into the equation:
(3x - 4) + (4x + 10) = 90
Simplifying:
7x + 6 = 90
Subtracting 6 from both sides:
7x = 84
Dividing both sides by 7:
x = 12
Now we can plug in x = 12 to find the measure of angle 2:
angle 2 = 4x + 10 = 4(12) + 10 = 58 degrees
Therefore, the measure of angle 2 is 58 degrees.
Which statement is true about angles 1 and 2?
3 lines intersect to form 6 angles. Clockwise, from top left, the angles 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3.