HELP ME ASAP PLEASE ITS THE SAME CONCEPT

Question

asked Dec 11, 2023 228k views

1 Answer

Dr Sokoban · Answer 1 · 2023-12-16T04:20:19+0000

Answer :

⠀

Explanation :

We know that,

⠀

Therefore,

⠀

${ \longrightarrow \sf \qquad \: m \angle \: P +m \angle Q + m\angle R = 180 {}^( \circ) }$

${ \longrightarrow \sf \qquad \: {(x + 13)}^( \circ) +{(10x + 13)}^( \circ) + {(2x - 2)}^( \circ) = 180 {}^( \circ) }$

⠀

Adding like terms we get :

${ \longrightarrow \sf \qquad \: {(x + 10x + 2x)} +(13^( \circ) + 13^( \circ) - 2^( \circ) ) = 180 {}^( \circ) }$

${ \longrightarrow \sf \qquad \: 13x +24^( \circ) = 180 {}^( \circ) }$

${ \longrightarrow \sf \qquad \: 13x = 180 {}^( \circ) - 24^( \circ) }$

${ \longrightarrow \sf \qquad \: 13x = 156 {}^( \circ) }$

${ \longrightarrow \sf \qquad \: x = \frac{156 {}^( \circ) }{13} }$

${ \longrightarrow \qquad \: { \pmb{ x = 12 {}^( \circ) } }}$

⠀

Therefore,

⠀

Now, Substituting the value of x in m∠Q :

⠀

${ \longrightarrow \qquad \: { \sf{ m \angle Q =( 10x + 13) {}^( \circ) } }}$

${ \longrightarrow \qquad \: { \sf{ m \angle Q =10(12) {}^( \circ) + 13{}^( \circ) } }}$

${ \longrightarrow \qquad \: { \sf{ m \angle Q =120 {}^( \circ) + 13{}^( \circ) } }}$

${ \longrightarrow \qquad \: { \pmb{ m \angle Q =133 {}^( \circ) } }}$

⠀