Question

Please solve this problem.​

Answer 1

Step-by-step 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,

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

$\sf \leadsto 3x + 7x + 5 + 5 = {180}^{\circ}$

$\sf \leadsto 10x + 5 + 5 = {180}^{\circ}$

$\sf \leadsto 10x + 10 = {180}^{\circ}$

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

$\sf \leadsto 10x = 170$

$\sf \leadsto x = \dfrac{170}{10}$

$\sf \leadsto x = 17$

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.