Question

Find the unknown angle in each of the following

Answer 1

Answer:

in a ,x=90-30=60

in b,x=180-25=55

in c,x=180-39+41=100

in d,x=180-47+21=112

Answer 2

★ How to do :-

Here, we are given with four diagrams in which two or three angles are forming a straight angle i.e, an angle of 180°. We are not given the value of one angle in each of the diagrams which written in the variable form 'x'. We are asked to find the value of those angles which are written as 'x'. We can see that the angles are forming a straight line. In which we should use the straight angle property to find out the answer. So, let's solve!!

$\:$

➤ Solution (1) :-

${\tt \leadsto \angle{1} + \angle{2} + \angle{3} = {180}^{\circ}}$

Substitute the values of those angles.

${\tt \leadsto {90}^{\circ} + x + {30}^{\circ} = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\tt \leadsto 90 + x + 30 = 180}$

Add the given values of the straight angle.

${\tt \leadsto 120 + x = 180}$

Shift the number 120 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 120}$

Subtract to get the value of 'x'.

${\tt \leadsto \orange{\underline{\boxed{\tt x = {60}^{\circ}}}}}$

$\:$

➤ Solution (2) :-

${\tt \leadsto \angle{1} + \angle{2} = {180}^{\circ}}$

Substitute the values.

${\tt \leadsto {25}^{\circ} + x = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\tt \leadsto 25 + x = 180}$

Shift the number 25 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 25}$

Subtract to get the value of 'x'.

${\tt \leadsto \orange{\underline{\boxed{\tt x = {155}^{\circ}}}}}$

$\:$

➤ Solution (3) :-

${\tt \leadsto \angle{1} + \angle{2} + \angle{3} = {180}^{\circ}}$

Substitute the values.

${\tt \leadsto {41}^{\circ} + x + {39}^{\circ} = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\tt \leadsto 41 + x + 39 = 180}$

Add the given values.

${\tt \leadsto 80 + x = 180}$

Shift the number 80 from LHS to RHS changing it's sign

${\tt \leadsto x = 180 - 80}$

Subtract to get the value of 'x'.

${\tt \leadsto \orange{\underline{\boxed{\tt x = {100}^{\circ}}}}}$

$\:$

➤ Solution (4) :-

${\tt \leadsto \angle{1} + \angle{2} + \angle{3} = {180}^{\circ}}$

Substitute the values.

${\tt \leadsto {21}^{\circ} + {47}^{\circ} + x = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\tt \leadsto 21 + 47 + x = 180}$

Add the given values.

${\tt \leadsto 68 + x = 180}$

Shift the number 68 from LHS to RHS changing it's sign.

${\tt \leadsto x = 180 - 68}$

Subtract to get the value of 'x'.

${\tt \leadsto \orange{\underline{\boxed{\tt x = {112}^{\circ}}}}}$

$\:$

Hence solved !!