Given: < WXZ = 90 degrees ( Right angle is an angle of 90 degree measure).
m< WXV = 11 more than 3 times m< WXY = (3 * <WXY + 11)
m< YXV = 139 degree.
To find : m<YXZ = ?
Solution : m< WXZ is equal to 90 degrees and is also the sum of angles m<WXY and m<YXZ i.e.
m< WXZ = 90 degrees = m<WXY + m<YXZ -----(1)
m< WXV = (3 * <WXY + 11) -----(2)
m <YXV is equal to 139 degrees and also equal to the sum of angles m<WXY and m<WXV i.e.
m <YXV = 139 degree = m<WXY + m<WXV -----(3)
Substituting m< WXV = (3 * <WXY + 11) from equation (2) in equation (3)
139 degree = m<WXY + m<WXV
=> 139 = m<WXY + 3 * m<WXY + 11 (Subtracting 11 from both sides)
=> 139 -11 = m<WXY + 3 * m<WXY + 11 -11
=> 128 = 4<WXY (Adding m<WXY + 3 * m<WXY)
=> 32 = < WXY (Dividing both sides by 4)
Substituting < WXY = 32 from above in equation (1)
90 degrees = m<WXY + m<YXZ
90 = 32 + m<YXZ (Subtracting 32 from both sides)
90-32 = 32 + m<YXZ -32
58 = m<YXZ.
Therefore, <YXZ =58 degrees.
