Question

Please answer this math question. The following figures are not drawn to scale. Find the unknown angles.​

Answer 1

a)<F + <G + <H = 180°

26° + 15° + <H = 180°

<H = 180° - 41°

<H = 139°

b)

<P + <S + <Q = 180°

60° + 32° +(50°+<RQS) = 180°

<RQS = 180°-142°

<RQS =38°

Answer 2

$\huge\mathbb{A~N~S~W~E~R}$

( I denote angle as L )

Find L FGH :-

In ∆FGH ,

L FGH + L GHF + L HFG = 180°

( angle sum property )

L FGH + 26° + 15° = 180°

L FGH = 180° - 41°

$</strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>L</strong><strong>~</strong><strong>F</strong><strong>G</strong><strong>H</strong><strong>~</strong><strong>=</strong><strong>~</strong><strong>4</strong><strong>1</strong><strong>°</strong><strong>}</strong><strong>$

Find L RQS :-

In ∆RQS,

L RQS + L QPS + L QSP = 180° ( || )

L PQR + L RQS + L QPS + L QSP = 180°

50° + L RQS + 60° + 32° = 180°

L RQS = 180° - 142°

[tex]\boxed{L~ RQS~ =~ 38°}[/tex】

${\huge\color{Red}</strong><strong>{</strong><strong>L</strong><strong>~</strong><strong>F</strong><strong>G</strong><strong>H</strong><strong>~</strong><strong>=</strong><strong>~</strong><strong>4</strong><strong>1</strong><strong>°</strong><strong> }}$

${\huge\color{Red}{</strong><strong>L</strong><strong>~</strong><strong>R</strong><strong>Q</strong><strong>S</strong><strong>~</strong><strong>=</strong><strong>~</strong><strong>3</strong><strong>8</strong><strong>°</strong><strong> }}$

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