Question

Measurement of one angle of a complementary angle is 10° more than another angle,

then what will be the measurement of the both the angles?​

Answer 1

Answer:

40

Step-by-step explanation:

Let the angle is x

The angle differs from the complement is x+10

The angle is ,

x+(x+10)=90

2x=90–10

x=40

Answer 2

★ How to do :-

Here, we are given that two angles are forming an angle of 90° i.e, a complementary angle. We are said that one of the angle is 10° greater than the other angle. We are asked to find the measurement of both the angles. So, here we should consider the smaller angle as a ny variable, let's say x. The concept of transportation of numbers from one side to other can be helpful here. Remember that, while shifting the numbers from one place to other we should change their signs. So, let's solve!!

$\:$

➤ Solution :-

Measure of smaller angle :-

${\tt \leadsto x + (x + 10) = {90}^{\circ}}$

Remove the bracket and add the common variables.

${\tt \leadsto 2x + 10 = 90}$

Shift the number 10 from LHS to RHS, changing it's sign.

${\tt \leadsto 2x = 90 - 10}$

Subtract the numbers on RHS.

${\tt \leadsto 2x = 80}$

Shift the number 2 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{80}{2}}$

Simplify the obtained fraction.

${\tt \leadsto \cancel \dfrac{80}{2} = \pink{\underline{\boxed{\tt x = {40}^{\circ}}}}}$

$\:$

Now, let's find the greater angle by using the given hint in question.

Measurement of bigger angle :-

${\tt \leadsto x + 10}$

Substitute the value of x.

${\tt \leadsto 40 + 10}$

Add the values to get the value of greater angle.

${\tt \leadsto \pink{\underline{\boxed{\tt {50}^{\circ}}}}}$

$\:$

Hence solved !!