What is the measure of 1 in the trapezoid? 110° 55° 165° 85°
2 answers:
Answer: The correct option is (B) 55°.
Step-by-step explanation: We are given to find the measure of angle 1 in the trapezoid shown in the figure.
We know that
one pair of sides of a trapezoid are parallel to each other.
As shown in the figure, the base of the trapezoid and its opposite side are parallel to each other.
Also, they are cut by a tranversal such that the angle 1 and the angle with measure 125° are interior angles on the same side of the transversal.
So, the sum of the measures must be equal to 180°.
That is,
Thus, the required measure of angle 1 is 55°.
Option (B) is CORRECT.
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Answer:
(-2, 4, -2)
x=-2, y=4, z=-2.
Step-by-step explanation:
So we have the three equations:
And we want to find the value of each variable.
To solve this system, first look at it and consider what you should try to do.
So we can see that the second and third equations both have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.
Therefore, let's first isolate the variable in the second and third equation.
Second Equation:
First, divide everything by -2 to simplify things:
Subtract x from both sides. The xs on the left cancel:
Now, divide everything by -2 to isolate the z:
So we've isolated the z variable. Now, do the same to the y variable in the third equation:
Subtract x from both sides:
Divide both sides by 2:
Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:
Distribute the third term. The -2s cancel out:
Since there is still a fraction, multiply everything by 2 to remove it:
Distribute:
Combine like terms:
Add 2 to both sides:
Divide both sides by 7:
Therefore, x is -2.
Now, plug this back into the second and third simplified equations to get the other values.
Second equation:
Third equation:
Therefore, the solution is (-2, 4, -2)