Question
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Part 1
angle1 and angle2 are complementary angles. The measure of angle1 is 30degrees. The measure of angle2 is 4xdegrees. Find the value of x. The figure is not drawn to scale.
12
Three rays start at the same point and form two angles. The first ray is vertical pointing upward. The second ray is horizontal pointing to the right. The third ray is between the first two rays and rises from left to right. The point where the vertical ray and the horizontal ray meet is marked with a small square. The angle formed by the vertical ray and the rising ray is labeled 2. The angle formed by the horizontal ray and the rising ray is labeled 1.
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Part 1
The value of x is
Answers
Answered by
GPT-4o mini
To find the value of \( x \) in the problem, we first need to use the fact that complementary angles sum up to \( 90^\circ \).
We are given:
- The measure of angle1 is \( 30^\circ \).
- The measure of angle2 is \( 4x \) degrees.
Since angle1 and angle2 are complementary, we can set up the following equation:
\[
30^\circ + 4x = 90^\circ
\]
Now, solve for \( x \):
1. Subtract \( 30^\circ \) from both sides of the equation:
\[
4x = 90^\circ - 30^\circ
\]
\[
4x = 60^\circ
\]
2. Divide both sides by \( 4 \):
\[
x = \frac{60^\circ}{4}
\]
\[
x = 15
\]
Therefore, the value of \( x \) is \( 15 \).
We are given:
- The measure of angle1 is \( 30^\circ \).
- The measure of angle2 is \( 4x \) degrees.
Since angle1 and angle2 are complementary, we can set up the following equation:
\[
30^\circ + 4x = 90^\circ
\]
Now, solve for \( x \):
1. Subtract \( 30^\circ \) from both sides of the equation:
\[
4x = 90^\circ - 30^\circ
\]
\[
4x = 60^\circ
\]
2. Divide both sides by \( 4 \):
\[
x = \frac{60^\circ}{4}
\]
\[
x = 15
\]
Therefore, the value of \( x \) is \( 15 \).