Question

the ratio of the measure of the three angles in a triangle is 10:3:7 find the measure of the largest angle

Answer 1

Answer:-

The three angles are in ratio 10:3:7.

Let the angles be 10x , 3x, 7x.

We know that,

Sum of angles of triangle = 180°

10x + 3x + 7x = 180°

20x = 180°

x = 180°/20

x = 9...

Now,

To find the largest angle,

i.e.

10x = 10 × 9

=> 90° ..... ans

_________________________________________________

@Miss_Solitary ✌️

Answer 2

AnswEr-:

• $\underline{\frak{\red{ \dag{ The\:Measures \:of\:largest \:angle \:of\:Triangle \:is\: \bf{90^{⁰} } \: , respectively. }}}}$

Explanation-:

$\mathrm {\bf{ Given-:}}$

• The ratio of the measure of the three angles in a triangle is 10:3:7.

$\mathrm {\bf{ To\:Find-:}}$

• The measure of largest angle of triangle.

$\sf{\bf{ \dag{ Solution \:of\:Question \:-:}}}$

$\mathrm {\bf{ Let's\:Assume\:-:}}$

• The measure of the three angles in a triangle be 10x , 3x and 7x .

Therefore ,

$\mathrm{\bf{\purple {Measures \:of\:Angles \:\: -:}}} \begin{cases} \sf{\blue{\angle \:A \:or\:First \:Angle \:\:= \frak{10x{⁰}}}} & \\\\ \sf{\pink{\angle \:B \:or\:Second\:Angle \:\: \:=\:\frak{3x^{⁰}}}} & \\\\ \sf{\red{\angle \:C \:or\:Third\:Angle \:\: \:=\:\frak{7x^{⁰}}}}\end{cases}$

$\underbrace{\underline { \mathrm { Understanding \:The\:Concept \:-:}}}$

• We have to find the largest angle of triangle when we have given the ratios of three angles of triangle.

• As , We know that ,

• The sum of all angles of triangles is 180⁰ or $\sf{ \angle A + \angle B + \angle C = 180^{⁰}}$

• By Putting we can get measures of all angles of triangles and from that ,

• We can find the Largest angle of Triangle

__________________________________________

$\sf{\bf{ \dag{ Finding \:Measures \:of\:all\:angle \:of\:Triangle \:-:}}}$

As , We know that ,

• $\underline{\boxed{\star{\sf{\red{  The\:Sum\:of\:measures\:of\:all\:angles\:of\:triangle\:is\:180^{⁰}.}}}}}$

Or ,

• $\underline{\boxed{\star{\sf{\red{\angle A + \angle B + \angle C =  \:180^{⁰}.}}}}}$

• $\mathrm{\bf{\purple {Here \:\: -:}}} \begin{cases} \sf{\blue{\angle \:A \:or\:First \:Angle \:\:= \frak{10x{⁰}}}} & \\\\ \sf{\pink{\angle \:B \:or\:Second\:Angle \:\: \:=\:\frak{3x^{⁰}}}} & \\\\ \sf{\red{\angle \:C \:or\:Third\:Angle \:\: \:=\:\frak{7x^{⁰}}}}\end{cases}$

Now , By Putting known Values -:

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ \angle A + \angle B + \angle C =  \:180^{⁰}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ 10x + 3x + 7x =  \:180^{⁰}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ 13x + 7x =  \:180^{⁰}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ 20x =  \:180^{⁰}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ x =  \:\dfrac{180}{20}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\longmapsto{\sf{ x =  \:\dfrac{\cancel {180}^{9}}{\cancel{20}}.}}$

$\qquad\quad\quad \qquad\quad \qquad\quad\underline{\boxed{\pink{\frak{ x =  \:9^{⁰}.}}}}$

____________________________________________

Now , By Putting x = 9 -:

• $\mathrm{\bf{\purple {Measures \:of\:Angles \:\: -:}}} \begin{cases} \sf{\blue{\angle \:A \:or\:First \:Angle \:\:= \frak{10x= 10 \times 9 = 90 {⁰}}}} & \\\\ \sf{\pink{\angle \:B \:or\:Second\:Angle \:\: \:=\:\frak{3x= 3 \times 9 = 27^{⁰}}}} & \\\\ \sf{\red{\angle \:C \:or\:Third\:Angle \:\: \:=\:\frak{7x= 7 \times 9 = 63^{⁰}}}}\end{cases}$

Therefore,

• $\underline{\frak{\pink{ \dag{ \:Measures \:of\:all\:angle \:of\:Triangle \:are\: \bf{90^{⁰} , 27^{⁰} \:and\;63^{⁰}} \: , respectively. }}}}$

Hence ,

• $\underline{\frak{\red{ \dag{ The\:Measures \:of\:largest \:angle \:of\:Triangle \:is\: \bf{90^{⁰} } \: , respectively. }}}}$

______________________________________________

$\large{\boxed{\mathrm {\bf{ |\:\:{\underline {More \:to\:Know \:-:}}\:\:| }}}}$

Some Properties of Triangle-:

• A Triangle always has three sides and three angles .

• The sum of all interior angles of Triangle is 180⁰

• The sum of two sides of Triangles is always greater than the third side of triangle .

• Formula for Area of Triangle-: ½ × Base × Height

_______________________________________________