Question

Please solve this problem.​

Answer 1

Explanation:

★ Solution :-

To find the value of x, we use a concept called as "The sum of interior angles on same side of transversal always measures 180° when added together".

Value of x :-

According to the concept,

`\sf \leadsto (3x + 5) + (7x + 5) = {180}^(\circ)`

`\sf \leadsto 3x + 7x + 5 + 5 = {180}^(\circ)`

`\sf \leadsto 10x + 5 + 5 = {180}^(\circ)`

`\sf \leadsto 10x + 10 = {180}^(\circ)`

`\sf \leadsto 10x = 180 - 10`

`\sf \leadsto 10x = 170`

`\sf \leadsto x = (170)/(10)`

`\sf \leadsto x = 17`

Now, let's find each of the angles.

Measurement of first angle :-

`\sf \leadsto 3x + 5`

`\sf \leadsto 3(17) + 5`

`\sf \leadsto 51 + 5`

`\sf \leadsto \angle{1} = {56}^(\circ)`

Measurement of second angle :-

`\sf \leadsto 7x + 5`

`\sf \leadsto 7(17) + 5`

`\sf \leadsto 119 + 5`

`\sf \leadsto \angle{2} = {124}^(\circ)`

Measurement of third angle :-

`\sf \leadsto Straight \: line \: angle = {180}^(\circ)`

`\sf \leadsto {56}^(\circ) + \angle{3} = {180}^(\circ)`

`\sf \leadsto \angle{3} = 180 - 56`

`\sf \leadsto \angle{3} = {124}^(\circ)`

Measurement of fourth angle :-

`\sf \leadsto Straight \: line \: angle = {180}^(\circ)`

`\sf \leadsto {124}^(\circ) + \angle{4} = {180}^(\circ)`

`\sf \leadsto \angle{4} = 180 - 124`

`\sf \leadsto \angle{4} = {56}^(\circ)`

Therefore, the ∠1, ∠2, ∠3 and ∠4 measures 56°, 124°, 56° and 124° respectively. The value of x is 17.