Question

Help me with this math assignment thanks

Answer 1

$\huge \star \: \underline\red{ \sf \bold{solution :} }$

⍟ solving 1. fig. :

$\\ \large \: \star \: \underline \bold{vertically \: \: opposite} \: \star\\ \\ \large \tt \mapsto \: \angle 1 = \angle 3 \\ \large \tt \mapsto \: \angle 2 = \angle 4 \\ \large \tt \mapsto \: \angle 5= \angle 7\\ \large \tt \mapsto \: \angle6 = \angle 8$

$\\ \large \: \star \: \underline \bold{alternate \: \: angles} \: \star\\ \\ \large \tt \mapsto \: \angle 3 = \angle 5 \\ \large \tt \mapsto \: \angle 2 = \angle 8 \\ \large \tt \mapsto \: \angle 4= \angle 6\\ \large \tt \mapsto \: \angle1 = \angle 7$

⍟ From above :

$\\ \large \tt \star \: \: \purple{\angle 1 = \angle 3 = \angle 5 = \angle 7} \\ \\ \large \tt \star \: \: \purple{ \angle 2 = \angle 4 = \angle 6 = \angle 8}$

$\large \: \star \: \underline \bold{linear \: \: pair} \: \star \\ \\ \large \tt \implies\angle1 + \angle2 = 180 \degree$

$\large \tt \implies \: 76 \degree + \angle2 = 180 \degree \\ \large \tt \implies \: \angle2 = 180 \degree - 76 \degree \\ \\ \large \star \: \underline{\boxed{ \therefore \tt \: \angle2 = 104 \degree}} \: \star$

⍟ Answers :

$\\ \large \tt \star \: \: \green{\angle 1 = \angle 3 = \angle 5 = \angle 7 = \pink{ 76 \degree}} \\ \\ \large \tt \star \: \: \green{ \angle 2 = \angle 4 = \angle 6 = \angle 8 = \pink{104 \degree}}$

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$\\ \large \star \: \: \underline{\underline{ \bold{given : }}} \\ \\ \large \tt \leadsto \: \angle1 = 10x + 2 \\ \large \tt \leadsto \: \angle2 = 3x + 9$

$\large \: \star \: \underline \bold{linear \: \: pair} \: \star \\ \\ \large \tt \implies\angle1 + \angle2 = 180 \degree$

$\large \tt \implies \: 10x + 2 + 3x + 9 = 180 \degree \\ \large \tt \implies \: 13x + 11 = 180 \degree \\ \large \tt \implies \: 13x = 180 \degree \\ \\ \large \implies \tt \: x = \frac{169 \degree}{13} \\ \\ \large \underline{ \boxed{ \tt \blue{\: x = 13 \degree}}}$

$\\ \large \star \: \: \underline{\underline{ \bold{answers : }}} \\ \\ \large \tt \leadsto \: \green{ \angle1 = 10(13) + 2 = \pink{ 132}} \degree \\ \large \tt \leadsto \green{ \: \angle2 = 3(13) + 9 = \pink{48 \degree}}$