Question

find the values of x y and z in the following diagrams.Best answer will be marked as the brainliest ​

Answer 1

$\boxed{\textbf{\large{Step-by-step explanation}}}$

◼ In the figure (1)

let us consider the angle be m whose measure is 135°

/_ z + /_m = 180° .....(linear pair)

/_ z = 180° - 135°

/_ z = 45°

◼As we know if the angles are of linear pair their sum is 180°, i.e..supplementary

Now if we consider the angle,

/_ y = /_ m = 135°

/_y = 135°

....(vertically opposite angles)

Now, /_x will be,

/_ x + /_y = 180°

/_ x + 135° = 180°

/_x = 180° - 135°

/_x = 45°

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Now, figure (2)

◼let us consider the angle be m whose measure is 31°

/_ y + /_ m = 90°

........(complementary angles)

◼complementary angles are the angles which , their sum will be 90°

/_ y + 31° = 90°

/_ y = 90° - 31

/_ y = 59°

Now, /_y = /_z

......(vertically opposite angles )

/_y = /_z = 59°

/_z = 59°

Also /_x = /_m = 31°

/_x = 31°

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Now, figure (3)

◼Angle whose measure is 51° considered as /_m and angle whose measure 44° considered as /_n

therefor,

/_x = /_ n = 44°

...( vertically opposite angles)

/_ x = 44°

Also, /_ z = /_m = 51°

.........( vertically opposite angles)

/_ z = 51°

Therefor, /_x + /_y +/_z = 180°

.....( linear pair)

◼we have already the measures of/_x and /_ z, we have to find the measure of /_y = ?

◼So, substitute the measures of /_xand /_z

/_x + /_y +/_z = 180

44° + 51° + /_y = 180°

95° + /_ y = 180°

/_ y = 180° - 95°

/_ y = 85°

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