Question

 If one angle of a triangle is 56' and the difference of the other two angles is 20', then find the other two angles. 
​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Let x ,y and z are three angles of a triangle .

/* According to the problem given,

Let x = 65° , y-z = 20 ---(1)

x + y + z = 180° /* Angle sum property */

=> 65° + y + z = 180°

=> y + z = 180° - 65°

=> y + z = 115° ---(2)

/* Add equations (1) and (2) , we get

2y = 135°

\implies y = \frac{135}{2}⟹y= 2135

\implies y = 67.5⟹y=67.5

/* Substitute y = 67.5 in equation (2) ,we get

67.5 + z = 11567.5+z=115

\implies z = 115 - 67.5 = 47.5⟹z=115−67.5=47.5

Therefore.,

\begin{gathered}Required \:two \: angles \: of \: triangle \:are\\67.5 \: and \: 47.5\end{gathered}

Requiredtwoanglesoftriangleare

67.5and47.5

Answer 2

$\sf{\bold{\purple{\star{\underline{\underline{Given}}}}}}$

• One angle of a triangle = 56°
• Diff. btw other 2 angles = 20°

⠀⠀⠀⠀

$\sf{\bold{\purple{\star{\underline{\underline{To\: find}}}}}}$

⠀⠀⠀⠀

• Other 2 unknown angles = ??

⠀⠀⠀⠀

$\sf{\bold{\purple{\star{\underline{\underline{Solution}}}}}}$

⠀⠀⠀⠀

• Let the angle be x

⠀⠀⠀⠀

• Other angle = x + 20

⠀⠀⠀⠀

$\sf{\star{\boxed{\orange{\frak{ Sum\: of \: all \: all \: angles\: of \: triangle = \: 180}}}}}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x + x + 20+ 56 = 180 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x + x + 76 = 180 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ 2x + 76 = 180 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ 2x = 180 - 76 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ 2x = 104 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x = \dfrac{104}{2}}}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x = 52 }}$

⠀⠀⠀⠀

$\sf{\star{\boxed{\blue{\frak{ x = 52 }}}}}$

⠀⠀⠀⠀

• putting value of x in angles

⠀⠀⠀⠀

1st unknown angle = x = $\sf{\dag{\boxed{\pink{\frak{ 52 }}}}}$

⠀⠀⠀⠀

2nd unknown angle = x + 20 = 52 + 20 = $\sf{\dag{\boxed{\pink{\frak{ 72 }}}}}$