The measure of angle ZWZX is approximately 43.22 degrees.
XW is not an altitude.
1. Use the angle bisector theorem:*The angle bisector theorem states that the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the measures of the two angles it divides. In this case, we can write the following equation:
XZ / ZY = (4x + 6) / (3x - 5)
2. Solve for x: We can cross-multiply the equation above to get:
XZ * (3x - 5) = ZY * (4x + 6)
Simplifying this equation, we get:
Factoring this equation, we get:
(3x + 2)(4x - 15) = 0
Therefore, x = -2/3 or x = 15/4.
3. Find the measure of angle ZWZX:*Since XW is an angle bisector, it divides angle ZYX into two smaller angles: WZX and WXY. We can use the following equations to find their measures:
m<WZX = (1/2) * m<ZYX = (1/2) * (4x + 6) = 2x + 3
m<WXY = (1/2) * m<ZWXY = (1/2) * (3x - 5) = (3x - 10) / 2
Now, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle ZWZX:
m<ZWZX + m<WXY + m<ZYX = 180 degrees
(2x + 3) + ((3x - 10) / 2) + (4x + 6) = 180 degrees
9x - 1 = 180 degrees
9x = 181 degrees
x = 20.11 degrees (approximately)
Therefore, the measure of angle ZWZX is approximately 2x + 3 = 43.22 degrees (approximately).
4. Determine if XW is an altitude: An altitude in a triangle is a line segment that passes through a vertex and is perpendicular to the opposite side. We can see from the diagram that XW does not intersect side YZ at a right angle. Therefore, XW is not an altitude.
The measure of angle ZWZX is approximately 43.22 degrees.
XW is not an altitude.
question: XW is an angle bisector, m ZYXZ = (4x + 6)°, m ZWXY= (3x – 5)°, and m ZXZY= (8x)°. Find mZWZX. Is XW an altitude? Y W Z O 32°; no O 62°; no O 64°; no 0 61°; yes