Question

pls solve this problem​

Answer 1

$\underline{ \underline{ \maltese \: \bold \red{from \: the \: diagram\: we \: get \: to \: know : }}}$

$\underbrace{\blacktriangleright\bold{all \: the \: angles \: written \: below\: will \: be \: equal \: }}$

$\bullet \: \angle \: 1 = \angle \: 4 \\ \leadsto \rm \: reason : \: alternate \: interior \: angles$

$\bullet \: \angle \: 3= \angle \: 2\\ \leadsto \rm \: reason : \: alternate \: interior \: angles$

$\bullet \: \angle \: 1 = \angle \: 2\\ \leadsto \rm \: reason : \:co - \: interior \: angles$

The sum of co - interior angle measures 180°

$\pmb{ \frak{ \: now \: lets \: solve \: it}}$

$\Rrightarrow \angle \: 1 + \angle \: 2 = 180 \degree \\ \Rrightarrow \: 3x + 5 + 7x + 5 = 180 \degree \\ \Rrightarrow \: 10x + 10 = 180 \degree$

$\Rrightarrow \: 10x = 180 \degree - 10 \\ \Rrightarrow \: 10x = 170 \degree \\ \Rrightarrow \: x = \frac{170}{10}$

$\longmapsto \overline{\fbox \pink{ \: x = 17}}$

$\sf \dagger \: now \: lets \: find \: \angle \: 1$

$\to \angle \: 1 = (3x + 5) \\\to\angle \: 1 = (3 \times 17)+ 5 \\ \to \: \angle \: 1 = 51 + 5 \bold{= \underline{56}}$

$\angle \: 1 = \angle \: 4 \\ \leadsto \fbox \color{blue}{56\degree}$

$\circ \sf \: reason : alternate \: interior \: angles$

$\sf \dagger \: now \: lets \: find \: \angle \: 2$

$\to \: \angle \: 2 = (7x + 5) \\ \to \angle \: 2 = (7 \times 17) + 5 \\ \to \: \angle \: 2 = 119 + 5 = \underline\bold{124}$

$\angle \: 2 = \angle \: 3 \\ \leadsto \fbox \color{blue}{124\degree}$

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Answer 2

★ 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.