Question

In Fig. 6.13, lines AB and CD intersect at O. If
$∠$AOC + $∠$BOE = 70° and $∠$BOD = 40°, find
$∠$BOE and reflex $∠$COE.

$\red{\tt{show\: work!}}$​

Answer 1

${\tt{Question}}\: \purple☟$

In Fig. 6.13, lines AB and CD intersect at O. If $∠$AOC +$∠$BOE = 70° and $∠$BOD = 40°, find$∠$BOE and reflex $∠$COE.

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$\red&#9998{\underbrace{\tt{Answer}}}\: \orange☟$

⠀⠀$&#9679\purple{\bf{Including \:work }}\red{⇑}$

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$\red{\bold{Given࿐}}$

$∠$AOC + $∠$BOE =70°

$\purple{\boxed{\bf{To\:find}}}$

$∠$BOE and reflex $∠$COE.

$\red{\boxed{\tt{Solution}}}$⤵️

Since AB is a straight line,

∴ ∠AOC + ∠COE + ∠EOB = 180°

or (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)]

or ∠COE = 180° – 70° = 110°

∴ Reflex ∠COE = 360° – 110° = 250°

Also, AB and CD intersect at O.

∠COA = ∠BOD [Vertically opposite angles]

But ∠BOD = 40° [Given]

∴ ∠COA = 40°

Also, ∠AOC + ∠BOE = 70°

∴ 40° + ∠BOE = 70° or ∠BOE = 70°-40° = 30°

$\blue{\boxed{\tt{Thus, ∠BOE = \:30°}}}$

$\red{\boxed{\bf{and}}}$

$\purple{\boxed{\tt{reflex\: ∠COE\: \:=250°}}}$

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$&#9679\orange{\bf{Question\: solved}}\: \green✔$

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All necessary formulas⤵️

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$\orange\star{\bf{\red{\underbrace{complementary \:angle}}}}\red\star$

The sum of 2 numbers$=90°$

example $a−b=90°$

how to find "a" if a is not mentioned

$\red{\underbrace{\bf{\orange{Given࿐}}}}$

$a= \: ?$

$b = 40$

$a+40=\:90°$

$a=90-40°$

$a=50°$

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$\pink\star{\bf{\purple{\underbrace{supplementary\: angle}}}}\red\star$

The sum of two numbers$= \:180°$

example $a+b=180°$

how to find "a" if a is not mentioned

Given

$a= \:?$

$b =\: 40$

$a+40=180°$

$a=180-40°$

$a=140°$

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$\orange\star{\bf{\green{\underbrace{Adjacent \:angle}}}}\red\star$

If there is a common ray between ${\bf&#x2220}a$ and ${\bf&#x2220}b$ so it is a adjacent angle.

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$\orange\star{\bf{\blue{\underbrace{Vertical\: opposite\: angle }}}}\red\star$

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

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$\orange\star{\bf{\orange{\underbrace{lenear\: pair \:of\: angles}}}}\red\star$

Here ${\bf&#x2220}a$$+{\bf&#x2220}b$$=$180°.

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