Question

Find the value of x . Please don't scam , if you don't know please don't answer , I will just report .​

Answer 1

116°

Step-by-step explanation:

< EDF=34° ( angle sum property of triangle)

angle ACB= 30° ( angle sum property )

x= 116° ( vertically opposite angle)

Answer 2

Answer:

116°

Step-by-step explanation:

Refer to the attachment for better understanding. Basically, ∠3 and x are vertically opposite angles. So, they'll be equal. We'll find the value of ∠3 to find the value of x. In order to find the measure of ∠3, we have to find the measure of ∠1 and ∠2 first.

○ Measure of ∠2 :

Consider the ∆ABC :

$\longrightarrow \sf{\quad { \angle A + \angle B + \angle C = 180^\circ}}$

○ Reason : Sum of all the interior angles of a triangle is 180°.

$\longrightarrow \sf{\quad { 35^\circ + 115^\circ + \angle 2 = 180^\circ}}$

Performing addition in LHS.

$\longrightarrow \sf{\quad { 150^\circ + \angle 2 = 180^\circ}}$

Now, transposing 150° from LHS to RHS. Its sign will get changed.

$\longrightarrow \sf{\quad { \angle 2 = 180^\circ - 150^\circ}}$

Performing subtraction in RHS.

$\longrightarrow \quad \boxed{\sf { \angle 2 = 30^\circ}}$

○ Measure of ∠1 :

Consider the ∆DEF :

$\longrightarrow \sf{\quad { \angle D + \angle E + \angle F = 180^\circ}}$

○ Reason : Sum of all the interior angles of a triangle is 180°.

$\longrightarrow \sf{\quad { \angle 1 + 100^\circ + 46^\circ = 180^\circ}}$

Performing addition in LHS.

$\longrightarrow \sf{\quad { 146^\circ + \angle 1 = 180^\circ}}$

Now, transposing 146° from LHS to RHS. Its sign will get changed.

$\longrightarrow \sf{\quad { \angle 1 = 180^\circ - 146^\circ}}$

Performing subtraction in RHS.

$\longrightarrow \quad \boxed{\sf { \angle 1 = 34^\circ}}$

Now,

Measure of ∠3 :

$\longrightarrow \sf{\quad { \angle 1 + \angle 2 + \angle 3 = 180^\circ}}$

○ Reason : Sum of all the interior angles of a triangle is 180°.

$\longrightarrow \sf{\quad { 34^\circ +30^\circ+ \angle 3 = 180^\circ}}$

Now, performing addition in the LHS.

$\longrightarrow \sf{\quad { 64^\circ+ \angle 3 = 180^\circ}}$

Now, transposing 64° from LHS to RHS. Its sign will get changed.

$\longrightarrow \sf{\quad { \angle 3 = 180^\circ - 64^\circ}}$

Performing subtraction in RHS.

$\longrightarrow \quad \boxed{\sf { \angle 3 = 116^\circ}}$

Now, as we know that, ∠3 and x are vertically opposite angles so they'll be equal. This implies that,

$\longrightarrow \quad \boxed{\sf { x = \angle 3 }}$

Substitute the value.

$\longrightarrow \quad \underline{\boxed{ \pmb{\mathfrak{x }} = \pmb{\mathfrak{116^\circ}}}}$

Therefore, measure of x is 116°.