1 thought on “the measure of two complementary angle s are in ratio 3:7 find the measure of the greater angle”
★ How to do :-
Here, we are given with the ratio of two angles that form a complementary angle i.e, an total angle of 90°. We are asked to find the measure of the greater angle among tt those two. So, first we should find the value of both the angles of this complementary angles. Then, we can find which is greater among both. Here, we are going to use the concept called as variables in which we use some variables and find the values of those. So, let’s solve!!
[tex]\:[/tex]
➤ Solution :-
[tex]{\tt \leadsto 3 : 7 = {90}^{\circ}}[/tex]
Apply a variable x on both part of ratios.
[tex]{\tt \leadsto 3x + 7x = {90}^{\circ}}[/tex]
Add both numbers having same variables.
[tex]{\tt \leadsto 10x = {90}^{\circ}}[/tex]
Shift the number 10 from LHS to RHS, changing it’s sign.
[tex]{\tt \leadsto x = \dfrac{90}{10}}[/tex]
Simplify the fraction to get the value of x.
[tex]{\tt \leadsto x = \cancel \dfrac{90}{10} = 9}[/tex]
[tex]\:[/tex]
Multiply the value of x to both part of the ratios to get the value of both angles.
★ How to do :-
Here, we are given with the ratio of two angles that form a complementary angle i.e, an total angle of 90°. We are asked to find the measure of the greater angle among tt those two. So, first we should find the value of both the angles of this complementary angles. Then, we can find which is greater among both. Here, we are going to use the concept called as variables in which we use some variables and find the values of those. So, let’s solve!!
[tex]\:[/tex]
➤ Solution :-
[tex]{\tt \leadsto 3 : 7 = {90}^{\circ}}[/tex]
Apply a variable x on both part of ratios.
[tex]{\tt \leadsto 3x + 7x = {90}^{\circ}}[/tex]
Add both numbers having same variables.
[tex]{\tt \leadsto 10x = {90}^{\circ}}[/tex]
Shift the number 10 from LHS to RHS, changing it’s sign.
[tex]{\tt \leadsto x = \dfrac{90}{10}}[/tex]
Simplify the fraction to get the value of x.
[tex]{\tt \leadsto x = \cancel \dfrac{90}{10} = 9}[/tex]
[tex]\:[/tex]
Multiply the value of x to both part of the ratios to get the value of both angles.
Measure of ∠1 :–
[tex]{\tt \leadsto 3x = 3 \times 9}[/tex]
[tex]{\tt \leadsto \angle{1} = {27}^{\circ}}[/tex]
Measure of ∠2 :-
[tex]{\tt \leadsto 7x = 7 \times 9}[/tex]
[tex]{\tt \leadsto \angle{2} = {63}^{\circ}}[/tex]
[tex]\:[/tex]
Here, we can observe that the measure of ∠2 is greater than the measure of ∠1. So,
[tex]{\sf \small \leadsto \pink{\boxed{\sf Measurement \: of \: greatest \: angle = {63}^{\circ}}}}[/tex]