Question

use the figure given below to find x+y+z .​

Answer 1

From the figure,

Consider the triangle MNO, We know that, sum of measures of interior angles of triangle is equal to 180

∘

.

∠M+∠N+∠O=180

∘

∠M+70

∘

+90

∘

=180

∘

160

∘

+∠M=180

∘

∠M=180

∘

−160

∠M=20

∘

We know that, sum of angles linear pair is equal to 180

∘

So, x+90=180

∘

By transposing we get,

x=180

∘

−90

∘

x=90

∘

Therefore, the value of x is 90

∘

.

Then, y+70

∘

=180

∘

By transposing we get,

y=180

∘

−70

∘

y=110

∘

Therefore, the value of y is 110

∘

.

Similarly, z+20=180

∘

By transposing we get,

z=180

∘

−20

∘

z=160

∘

Therefore, the value of z is 160

∘

.

Hence, x+y+z

=90

∘

+110

∘

+160

∘

=360

∘

Answer 2

Answer:

x = 180° – 75° [Co – interior angles]

= 105°

y = 180° – x [Co – interior angles]

= 180° – 105° = 75° [Corresponding angles]

z = 75°