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In the adjoining figure, there coplanar lines $AB, CD$ and $EF$ intersect at a point $O,$ forming angles as shown. Then the value of $x, y, z, t$ respectively are $°$ , $40 °$ , $50 °$ and $°$ .

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Detailed Solution

In the adjoining figure, there coplanar lines

AB, CD

and

EF

intersect at a point

O,

forming angles as shown. Then the value of

x, y, z, t

respectively are

40 °

40 °

50 °

and

90 °

.
It is given that

A B, C D, E F

intersect at

O

.
Evaluate

.
From the figure,
For z,

∠ C O E = ∠ D O F

(vertically opposite angles are equal)

∠ C O E = z = 50 °

For t,

∠ B O D = ∠ A O C

(vertically opposite angles are equal)
Since they are vertically opposite angles,

t = 90 °

.
Now, for x and y,

∠ B O E = ∠ F O A

(vertically opposite angles are equal)
Evaluate the value of

y

C O D

is a straight line.
Therefore,

are a linear angle

(180 °)

.
Hence,

.
Substitute the known values within the formula,

50 ° + 90 ° + ∠ B O E = 180 °

140 ° + y = 180 ° y = 40 °

∠ B O E = ∠ F O A

, (vertically opposite angles are equal)
Therefore,

∠ F O A = x ∠ F O A = 400

The angles are given by,

x = 40 °, y = 40 °, z = 50 °, t = 90 °

.
Hence the required answer is

x = 40 °, t = 90 °

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