Question

7.Find the measure of the angles of a triangle if the ratio of their measures is 4:12:29 ?

Answer 1

Answer :-

• Angles of the triangle = 16° , 48° and 116°

Step by step explanation:

To find :-

• Angles of the triangle.

Solution:

Given that,

• Ratio of angles of the triangle = 4:12:29.

Let the angles be 4x , 12x and 29x respectively.

We know,

• Sum of angles of a triangle = 180°.

Therefore,

$\longrightarrow \bf 4x + 12x + 29x = 180^{ \circ}$

ᅠ

$\longrightarrow \bf 45x = 180^{ \circ}$

ᅠ

$\longrightarrow \bf x = \dfrac{180}{45}$

ᅠ

$\longrightarrow \bf x = 4$

ᅠ

Therefore, Angles of the triangle are :-

• 4x = 4 × 4 = 16°
• 12x = 12 × 4 = 48°
• 29x = 29 × 4 = 116°

Answer 2

❍ Let the angles of the traingle be 4x, 12x and 29x respectively.

$\underline{\pink{\bigstar\:\boldsymbol{By\: Using\; ASP \; Property\::}}}$

• Angle Sum Property of Triangle is basically, sum of all angles of the triangle is 180°.

Therefore,

$\dashrightarrow\sf 4x + 12x + 29x = 180^\circ \\\\\\\dashrightarrow\sf 16x + 29x = 180^\circ \\\\\\\dashrightarrow\sf 45x = 180^\circ \\\\\\\dashrightarrow\sf x = \cancel\dfrac{180^\circ}{45} \\\\\\\dashrightarrow{\underline{\boxed{\frak{\pink{x = 4^\circ}}}}}$

Hence,

• First angle, 4x = 4(4) =16°

• Second angle, 12x= 12(5) = 48°

• Third angle, 29x = 29(4)° = 116°

$\therefore{\underline{\sf{Hence,\;angles\;of\;the\;\triangle\;are\; \bf{16^\circ,48^\circ\;\&\;116^\circ}.}}}$

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