An obtuse angle is formed by two adjacent angles with measures (x+10) degrees and (3x) degrees. if the resulting angle measure is 118 degrees, what is the angle measure of each of the unknown angles? Round to the nearest whole number
A. 43 and 75
B. 37 and 81
C. 20 and 98
D. 34 and 84
The sum of the measures of two adjacent angles forms a straight line or a 180-degree angle. Therefore, we can set up the equation: (x+10) + (3x) = 180.
Combining like terms, we get 4x + 10 = 180.
Subtracting 10 from both sides, we get 4x = 170.
Dividing both sides by 4, we get x = 42.5.
Therefore, the measure of the first angle is x+10 = 42.5+10 = 52.5 degrees.
The measure of the second angle is 3x = 3(42.5) = 127.5 degrees.
Out of the answer choices, the angles that are closest to these measures are option A: 43 and 75 degrees.
what is the simplified equation corresponding to the measure of the angles?
A.(3x-22)=90
B.(7x-22)=90
C.(3x-22)=180
D.(7x-22)=180
To find the simplified equation corresponding to the measure of the angles, we need to set up the equation using the given information.
We are told that the resulting angle measure is 118 degrees, so we have the equation: (x + 10) + (3x) = 118.
Combining like terms, we get 4x + 10 = 118.
Subtracting 10 from both sides, we get 4x = 108.
Dividing both sides by 4, we get x = 27.
Therefore, the simplified equation corresponding to the measure of the angles is: (3x + 10) + (3x) = 118.
Simplifying this equation further, we get 6x + 10 = 118.
a b c or d ?
Apologies for the confusion. The correct answer is:
D. (7x - 22) = 180
For two vertical angles with measure m<1 = (4x+26) degree and m <3=(3x+32), what is the measure of each angle
A.6
B.24
C.50
D.64
Vertical angles are congruent, meaning they have the same measure. So, we can set the two expressions for the measure of the angles equal to each other:
4x + 26 = 3x + 32
Subtracting 3x from both sides, we get:
x + 26 = 32
Subtracting 26 from both sides, we get:
x = 6
Now, we can substitute this value of x back into either of the expressions to find the measure of each angle. Let's use the expression 4x + 26:
Measure of angle 1 = 4(6) + 26 = 24 + 26 = 50 degrees
Therefore, the measure of each angle is:
Angle 1: 50 degrees
Angle 3: Since it is vertical to Angle 1, it also measures 50 degrees
The correct answer is C. 50