Question

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Answer 1

Answer:

The value of $x=7 and z=81$

Step-by-step explanation:

Given that lines are intersecting each other.

Figure show that labelled part

Angle AOD = $9x+36$

Angle DOC = z

Angle COB = 99

Here, Line AC is a straight line

We can write as,

Angle AOD+Angle DOC=180

$(9x+36)+z=180.$

Now, When two lines intersect each other, the corresponding opposite angle is equal.

Angle AOD=Angle COB

$9x+36=99$

$9x+36=99$

$9x=63$

$x=7$

Replacing the value of x in an equation (9x+36)+z=180.

$(9x+36)+z=180.$

$(9(7)+36)+z=180.$

$63+36+z=180$

$z=81$

Thus,

The value of x=7 and z=81

Answer 2

Answer:

Therefore,

$x= 7\\\\z= 81$

Step-by-step explanation:

Given:

Let label the angles first,

m∠ COA = (9x + 36)°

m∠ DOA = z°

m∠ DOB = 99°

To Find:

Value of

x = ?

z = ?

Solution:

Vertical Angles:

The angles opposite each other when two lines cross. They are always equal.

∴ m∠ COA = m∠ DOB

Substituting the given values we get

$(9x + 36)\°=99\°\\\\\therefore 9x=99-36\\\\\therefore x=\frac{63}{9}=7 \\\therefore x=7\ \textrm{as required}$

Linear Pair:

A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other, and supplementary means that the measures of the two angles add up to equal 180 degrees.

∴ m∠ DOB + m∠ DOA = 180°  ......{Linear Pair}

Substituting the given values we get

$99+z=180\\\\\therefore z=180-99\\\\\therefore z=81\° \textrm{as required}$

Therefore,

$x= 7\\\\z= 81$