The values of x, y and z are 95⁰, 51⁰ and 39⁰ respectively.
How to find x,y and z in the figure
Using the supplementary angles, straight line angles and complementary angles postulates.
From the given figure
23 + 62 + x = 180⁰(sum of angles in a triangle)
85 + x = 180
x = 180 - 85
= 95⁰
x + 34 + y = 180(angles on a straight line)
95 + 34 + y = 180
129 + y = 180
y = 180 - 129
= 51⁰
y + z = 90(complementary angles)
51 + z = 90
z = 90 - 51
z = 39⁰
The values of x, y and z are 95⁰, 51⁰ and 39⁰ respectively.