Question

tell the answer with explanation​

Answer 1

Solution -

Here , in the attached figure , OB is the bisector of Angle B and OC is the bisector of angle C .

Now , Angle BOC = 100°

In ∆ BOC -

=> Angle BOC + { Angle OBC + Angle OCB } = 180°

=> 100° + { Angle OBC + Angle OCB } = 180°

=> { Angle OBC + Angle OCB } = 180° - 100°

=> { Angle OBC + Angle OCB } = 80°

But ,

Angle OBC = Angle B / 2

Angle OCB = Angle C / 2 .

=> [ Angle B / 2 + Angle C /2 } = 80°

=> ½ [ Angle B + Angle C ] = 80°

=> Angle B + Angle C = 160°

Now , in ∆ ABC -

Angle A + Angle B + Angle C = 180°

=> Angle A + { Angle B + Angle C } = 180°

=> Angle A + 160° = 180°

=> Angle A = 20° .

Thus , the required value of angle A is 20°

_____________________________________

Answer 2

In the figure :-

$\bf\huge\green{\underline{\underline{Given :-}}}$

• $\bf{\angle} BOC = 100°$
• $\bf{bisectors \: of \: {\angle}ABC and {\angle}BCA \: meet \: at \: the \: point \: O}$

$\bf\huge\pink{\underline{\underline{To \: find:-}}}$

• $\bf{The \:unknown \:angle \: i.e., {\angle} A = ??}$

$\bf\bold{Let's \: find\: out }$

$\bf\huge\purple{Solution :- }$

✧ First step( with ∆ BOC) :-

• $\bf{Here, \: the \:{\angle}BOC = 100°}$
• $\bf{ The \:{\angle}OCB and {/angle}OBC are \: equal }$

$\bf{ Let's \:assume\: that {\angle}OBC\: is \: x }$

According to the question,

=> $\bf{\angle}OBC + {\angle}OCB + {\angle} COB = 180° (angle\: sum \:property)$

=>2x + 100° = 180°

=> x = 40°

$\bf{\therefore}{\angle}OBC and {\angle}OCB = 40°$

✧ Now, (In ∆ ABC ):-

$\bf\huge\orange{\underline{\underline{To \: find:-}}}$

• $\bf{the \: unknown \: angle{\angle}A = ??}$

$\bf {\angle}ABC \:\:and\:\: {\angle} BCA \:\:are\:\: bisected\: \:by\:\: {\angle}B$

$\bf{\therefore}{\angle}B and {\angle}C = 40° × 2 = 80°$

According to the question,

=> $\bf{\angle}A + {\angle}B + {\angle}C = 180°$

=> 80° + 80° + A = 180°

$\bf\huge\bold\purple{\boxed{\boxed{\underline{\underline<strong>=</strong><strong>></strong><strong> </strong><strong>A</strong><strong> </strong><strong>=</strong><strong> </strong><strong>2</strong><strong>0</strong><strong>°</strong>}}}}<strong> </strong>$