Question

The sum of the measures of angles m and angle l is 116 degrees.
The measure of angle m is 50 degrees
The measure of angle l is (7x - 4) degrees
What is the value of x?
10
12
15
20
Answer
Find the measure for <MQR
70-2b on left and 28 + 5b on right
Answer
58
60
62
64
Answer
5x degrees and (3x + 10) degrees
Find the measure
Answer
25
65
115
135
155
Answer
pick one
Answered by GPT 3.5
To find the value of x, we can set up an equation using the information given.

The sum of the measures of angles m and l is 116 degrees, so we have the equation:
m + l = 116

Given that m is 50 degrees and the measure of angle l is (7x - 4) degrees, we can substitute these values into the equation:
50 + (7x - 4) = 116

Simplifying this equation, we get:
7x + 46 = 116

Subtracting 46 from both sides, we have:
7x = 70

Finally, dividing both sides by 7, we find the value of x:
x = 10

Therefore, the value of x is 10.
Answered by GPT 3.5
To find the measure of angle <MQR, we need to find the value of b first.

We're given the following information:

The measure of the angle on the left of <MQR is 70 - 2b degrees.
The measure of the angle on the right of <MQR is 28 + 5b degrees.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:
(70 - 2b) + <MQR + (28 + 5b) = 180

Simplifying this equation, we have:
98 + 3b + <MQR = 180

Now, we can subtract 98 from both sides to isolate <MQR:
3b + <MQR = 82

To find the measure of angle <MQR, we need to know the value of b. If b is given, we can substitute that value into the equation to find the measure of <MQR.
Answered by GPT 3.5
To find the measure of angle <MQR, we can substitute the value of b as given.

If b is 58, we can substitute b = 58 into the equation:
3(58) + <MQR = 82

Simplifying this equation, we have:
174 + <MQR = 82

Subtracting 174 from both sides, we get:
<MQR = -92

Since angles cannot have negative measures, this solution is not valid.

Therefore, it seems there might be a mistake in the given information. Please double-check the values provided for the measures of the angles on the left and right of angle <MQR.
Answered by GPT 3.5
To find the measure of angle <MQR, we can substitute the given expressions for the measures of the angles on the left and right of angle <MQR.

The measure of the angle on the left of <MQR is 5x degrees.
The measure of the angle on the right of <MQR is (3x + 10) degrees.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:
(5x) + <MQR + (3x + 10) = 180

Simplifying this equation, we have:
8x + <MQR + 10 = 180

Now, we can subtract 10 from both sides to isolate <MQR:
8x + <MQR = 170

To find the measure of angle <MQR, we need to know the value of x. If x is given, we can substitute that value into the equation to find the measure of <MQR.
Answered by GPT 3.5
To find the measure of angle <MQR, we can substitute the value of x as given.

If x is 25, we can substitute x = 25 into the equation:
8(25) + <MQR = 170

Simplifying this equation, we have:
200 + <MQR = 170

Subtracting 200 from both sides, we get:
<MQR = -30

Again, angles cannot have negative measures, so this solution is not valid.

It appears there might be a mistake in the given information. Please double-check the values provided for the measures of the angles on the left and right of angle <MQR.
Answered by GPT 3.5
Sure, let's pick 115 as the value for the measure of angle <MQR.

If the measure of angle <MQR is 115 degrees, we can substitute this value into the equation:
8x + 115 = 170

Subtracting 115 from both sides, we get:
8x = 55

Dividing both sides by 8, we find the value of x:
x = 6.875

Therefore, if the measure of angle <MQR is 115 degrees, the value of x is approximately 6.875.