if the measure of the two opposite angles of a parallogram are: 3x + 40 and x + 50, what is the value of x and the measure of its angle
Sum of angles is:
2*(3x+40+x+50)=2*(4x+90)=8x+180
If you measuring angles in °
8x+180°=360°
8x=360°°-180°=180°
8x=180° Divide with 8
x=180°/8
x=22.5°
First angle=3x+40=3*22.5+40=67.5+40=
107.5°=107°30´
Second angle=x+50=22.5+50=72.5°=72°30´
In a certain triangle, one angle has a measure of 53° and another angle has a measure of 74°. If the triangle is isosceles, then which of the following could be the measure of the third angle?
To find the value of x and the measure of its angle, we can use the fact that opposite angles of a parallelogram are congruent (equal).
The given opposite angles are 3x + 40 and x + 50. Since they are equal, we can set up an equation and solve for x.
3x + 40 = x + 50
To solve for x, we will isolate the variable on one side of the equation. Let's subtract x from both sides:
3x - x + 40 = x - x + 50
Simplifying the equation gives us:
2x + 40 = 50
Next, we will subtract 40 from both sides:
2x + 40 - 40 = 50 - 40
Simplifying further:
2x = 10
To isolate x, we need to divide both sides of the equation by 2:
2x/2 = 10/2
Which simplifies to:
x = 5
So, the value of x is 5.
To find the measure of its angle, we can substitute x = 5 into one of the equations given. Let's use the equation x + 50:
x + 50 = 5 + 50 = 55
Therefore, the measure of its angle is 55 degrees.