YW is a bisector of <XYZ. <XYW = (8x - 5) and <WYZ = (6x + 17). Find the measure of the following angles.
1. < XYW =
2. < WYZ =
3. < XYZ =
1. To find the measure of angle XYW, we need to set up an equation using the fact that YW is a bisector of angle XYZ. Since YW bisects angle XYZ, we know that angle XYW is equal to angle WYZ.
So, we can set up the equation:
8x - 5 = 6x + 17
To solve for x, we can subtract 6x from both sides and then subtract 17 from both sides:
8x - 6x = 17 + 5
2x = 22
Dividing both sides by 2, we find:
x = 11
Now that we know the value of x, we can substitute it back into the equation to find the measure of angle XYW:
<XYW = 8x - 5 = 8(11) - 5 = 88 - 5 = 83 degrees.
Therefore, the measure of angle XYW is 83 degrees.
2. Since we know that angle XYW is equal to angle WYZ, the measure of angle WYZ is also 83 degrees.
Therefore, the measure of angle WYZ is 83 degrees.
3. Angle XYZ is the sum of angle XYW and angle WYZ. Since both angles are equal to 83 degrees, the measure of angle XYZ is twice that:
<XYZ = 2 * 83 = 166 degrees.
Therefore, the measure of angle XYZ is 166 degrees.
To find the measure of the angles, we need to set up an equation and solve for x. Once we find the value of x, we can substitute it back into the expressions for the angles to determine their measures.
1. <XYW = (8x - 5)
2. <WYZ = (6x + 17)
3. <XYZ = ?
Since YW is a bisector of <XYZ, it divides the angle into two congruent angles. Therefore, we can set up an equation:
<XYW = <WYZ
(8x - 5) = (6x + 17)
Now, let's solve for x:
8x - 5 = 6x + 17
2x = 22
x = 11
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures:
1. <XYW = (8x - 5) = (8 * 11 - 5) = 88 - 5 = 83 degrees
2. <WYZ = (6x + 17) = (6 * 11 + 17) = 66 + 17 = 83 degrees
3. <XYZ = 2 * <XYW = 2 * 83 = 166 degrees
solve 8x - 5 = 6x + 17
once you have x, sub back into the two expressions