Use the image to answer the question.
An illustration shows five rays emerging from a point labeled A, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.
If m∠2=47° , what is m∠4 ?
(1 point)
Since angles 1 and 2 together form a right angle, and angle 2 measures 47°, we can conclude that angle 1 measures 90° - 47° = 43°.
Similarly, since angles 2 and 4 together form a straight angle, we can conclude that angle 4 measures 180° - 47° = 133°.
Therefore, m∠4 = 133°.
Use the image to answer the question.
An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?
(2 points)
x°+
°=
°
We know that angles 5 and 8 are corresponding angles and are congruent. Therefore, m∠8 = m∠5 = 112°.
Since m∠8 = (2x+8)°, we can set up the following equation:
112° = 2x + 8°
To solve for x, we need to isolate the variable on one side of the equation. We can do this by subtracting 8° from both sides:
112° - 8° = 2x + 8° - 8°
104° = 2x
Now, we can divide both sides by 2 to solve for x:
x = 104° / 2
x = 52°
Therefore, the equation to solve for x is:
x° + 0° = 52°
u sure
Apologies for the mistake in my previous response. Let's find the correct equation to solve for x.
Since angles 5 and 8 are corresponding angles, we have:
m∠8 = m∠5 = 112°
And since m∠8 = (2x+8)°, we can set up the following equation:
112° = 2x + 8°
To solve for x, we need to isolate the variable on one side of the equation. We can do this by subtracting 8° from both sides:
112° - 8° = 2x + 8° - 8°
104° = 2x
Now, divide both sides by 2:
104° / 2 = 2x / 2
52° = x
Therefore, the correct equation to solve for x is:
x° + 0° = 52°
thats not right
Apologies for the confusion. Let's try solving the equation again.
We are given that m∠5 = 112° and m∠8 = (2x + 8)°.
Since angles 5 and 8 are corresponding angles, they are congruent. Therefore, we can set up the following equation:
m∠8 = m∠5
(2x + 8)° = 112°
To solve for x, we need to isolate the variable on one side of the equation. We can do this by subtracting 8 from both sides:
2x + 8 - 8 = 112 - 8
2x = 104
Now, divide both sides by 2:
(2x)/2 = 104/2
x = 52
Therefore, the correct equation to solve for x is:
x = 52
For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)
°
Vertical angles are formed by two intersecting lines. They are opposite each other and are congruent to each other.
Given that m∠1 = (2x + 26)° and m∠3 = (3x + 32)°, we have:
m∠1 = m∠3
(2x + 26)° = (3x + 32)°
To solve for x, we can solve this equation.
First, let's simplify the equation:
2x + 26 = 3x + 32
To isolate the variable, let's subtract 2x from both sides:
2x - 2x + 26 = 3x - 2x + 32
26 = x + 32
Next, let's subtract 32 from both sides:
26 - 32 = x + 32 - 32
-6 = x
Therefore, the value of x is -6.
To find the measure of each angle, substitute x = -6 into the equations:
m∠1 = (2x + 26)° = 2(-6) + 26 = 12 + 26 = 38°
m∠3 = (3x + 32)° = 3(-6) + 32 = -18 + 32 = 14°
So, the measure of each angle is 38°.