Question

two angles are in linear pair their measures are represented by X + 10 and X + 30 what are the measures of the angles​

Answer 1

Answer:

$\huge{\bf{\underline{\red{Answer :}}}}$

x + 30 + 3x - 10 = 180

4x + 20 = 180

4x = 160

x = 40

The angles are $\boxed{\orange{70°, 110° }}$

Answer 2

$\Huge\rm\green{an{\mathcal{S}}wer:}$

${}$

$\bf{{\underline{To~find}}:}$

• The unknown angles that form a linear pair

$\bf{{\underline{Here,~we~know~that}}:}$

• The sum of the angles that form a linear pair is 180°

$\sf : \implies (x + 10) + (x + 30) = 180 \degree \\ \sf : \implies 2x + 40 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies 2x = 180 - 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies 2x = 140 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies x = \frac{140}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies x = \green{ \underline{ \boxed{ \bf 70}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bf\therefore{{\underline{Required~angles}}:}$

$\sf x + 10 = 70 + 10 = \green{ \underline{ \boxed{ \bf 80 \degree}}} \: \: \\ \\ \sf x + 30 = 70 + 30 = \green{ \underline{ \boxed{ \bf 100 \degree}}}$

$\bf{{\underline{Verification}}:}$

$\sf 80 \degree + 100 \degree = \green{ \underline{ \boxed{ \bf 180 \degree}}}$