Question

If angles of a triangle are x °,2x° ,2x°.Find each angle of the triangle.

60°,60°,60°

36°,72°,72°

40°,40°,100°

​

Answer 1

Given:

• We're given with the angles of a triangle are x°, 2x° and 2x.

To find:

• We've to find out each angle of the triangle.

Solution: Let the angles of a triangle are x°, 2x° and 2x. ⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

⠀

• Sum of all angles of the triangle is 180°.

⠀

Therefore,

⠀

$:\implies\sf x + 2x + 2x = 180 \\\\\\:\implies\sf 5x = 180 \\\\\\:\implies\sf x = \cancel\dfrac{180}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 36}}}}}\;\bigstar$

⠀

❍As x = 36°, than all angles of the triangle are :

⠀

• First angle, x = 36°
• Second angle, 2x = 2(36) = 72°
• Third angle, 2x = 2(36) = 72°

⠀

$\therefore{\underline{\sf{Hence, \;angles\;of\;\triangle\;are\; \bf{Option\;b)\; 36^\circ, 72^\circ\;and\;72^\circ}.}}}$

⠀

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Answer 2

Given : Angles of a triangle are x° , 2x° and 2x° respectively.

To Find : Each angle of the triangle. ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

❍ Here, three angles of the triangle is given. We've to find the value of x as well all angles of the triangle.

$\: \:$

As we know that,

$\:$

❍ Sum of all angles of a triangle is 180°.

$\: \:$

$\star \: \: \underline{\boxed{\sf\pink{ \angle1 + \angle2 + \angle3 = 180 \degree}}}$

$\: \:$

Now,

$\: \:$

$\sf:\implies \: \angle1 + \angle2 + \angle3 = 180 \degree \\ \\ \\ \sf:\implies \: x + 2x + 2x = 180 \\ \\ \\ \sf:\implies \: 5x = 180 \\ \\ \\ \sf:\implies \: x = \cancel\frac{180}{5} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{x = 36 \degree}}} \: \bigstar \:$

$\: \:$

Now,

$\: \:$

• First angle = 36°
• Second angle = 2(36) = 72°
• Third angle = 2(36) = 72°

$\: \:$

$\: \:$

$\sf\therefore{\underline{Hence, \: all \: angles \: of \: the \: triangle \: are \: \bold{36 \degree} \: \bold{36 \degree} and \: \bold{72 \degree}}}$