Question

each of the two equal angle of a triangle is twice the third angle. Find the angle of triangle​

Answer 1

Given :-

• Two equal angles which are twice of third angle.

Two find :-

• Measure of all angle.

Assume that :-

• Third angle be x and other,
• Two equal angle will be 2x & 2x because they are equal to each other and twice of third angle.

[ We know that sum of all angle of triangle is 180°. ]

${\sf{\bigstar{ \: So, according \: to \: the \: question \: :}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: {\mathtt{\implies{2x + 2x + x = 180 \degree}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: {\mathtt{\implies{5x = 180 \degree}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: {\mathtt{\implies{x = \frac{180}{5} }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: { \boxed{ \boxed{ {\mathtt{\implies{x = 36 \degree}}}}}}$

${\sf{\bigstar{ \: So, all \: Angles \: of \: triangle \: are :}}}$

Putting the value of x :-

${\large{\mathtt{\leadsto{x = { \boxed{ \color{green}36 \degree}}}}}}$

${\large{\mathtt{\leadsto{2x \implies2 \times 36 \degree = { \boxed{ \color{green}72 \degree}}}}}}$

${\large{\mathtt{\leadsto{2x \implies2 \times 36 \degree = { \boxed{ \color{green}72 \degree}}}}}}$

So, all angles of triangle are 36°, 72° & 72°.

Answer 2

ɢɪᴠᴇɴ:-

• Each of the two equal angles of a triangle is twice the third angle.

ᴛᴏ ꜰɪɴᴅ:-

• The angles of the triangle.

ꜱᴏʟᴜᴛɪᴏɴ:-

Let, each equal angle of the triangle be x°

and, the third angle be y°

According to the given condition,

$\begin{lgathered}\begin{lgathered}\frak {x=2y} \\ \\\end{lgathered}\end{lgathered}$

As we know that,

$\begin{lgathered}\begin{lgathered}\frak {x+ x + y = 180^{\circ}} \\ \\\end{lgathered}\end{lgathered}$ (Angle Sum Property)

Now,

$\begin{lgathered}\begin{lgathered}:\implies\frak {2y + 2y + y = 180°^{\circ}} \\ \\\end{lgathered}\end{lgathered}$

$\begin{lgathered}\begin{lgathered}:\implies\frak {5y = 180^{\circ}} \\ \\\end{lgathered}\end{lgathered}$

$\begin{lgathered}\begin{lgathered}:\implies\frak {y= \dfrac{180^{\circ}}{5}} \\ \\\end{lgathered}\end{lgathered}$

$\begin{lgathered}\begin{lgathered}:\implies{\boxed{\frak{\pink{y = 36^{\circ}}}}}\;\bigstar\\ \\\end{lgathered}\end{lgathered}$

For finding the value of x,

$\begin{lgathered}\begin{lgathered}:\implies\frak {x = 2y} \\ \\\end{lgathered}\end{lgathered}$

$\begin{lgathered}\begin{lgathered}:\implies\frak {x = 2\times 36^{\circ}} \\ \\\end{lgathered}\end{lgathered}$

$\begin{lgathered}\begin{lgathered}:\implies{\boxed{\frak{\purple{x = 72^{\circ}}}}}\;\bigstar\\ \\\end{lgathered}\end{lgathered}$

Therefore, the angles are 72°, 72° and 36°.

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