Find the value of the variable.
66

32

29

43

The correct answer is x = 32.

Step-by-step explanation:

To solve this problem, we must remember the concept of supplementary angles.  Two angles that are supplementary together make an angle of 180 degrees (a straight line).

In this case, we can see that inside the triangle, we will have an angle of 80 degrees.  We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.

On the lower right hand of the triangle, a similar rationale can be applied.  The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.

Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees.  This lets us set up the following equation:

80+68+x = 180

Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.

148 + x = 180

Next, we should subtract 148 from both sides of the equation.

x = 180-148

x = 32

Therefore, the correct answer is x = 32 degrees.

Hope this helps!  

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

where is the picture

step-by-step explanation: