Question

The angles are complementary and the angle is 40 degree less than the larger​

Answer 1

Answer:

let the larger number be x

then the smaller angle will be x-40

so

x+x-40=90

2x-40=90

2x=90+40

2x=130

x=130/2

x=65

then

x-40=65-40

x-40=25

Answer 2

Question :-

• Two angles are complementary and the smaller angle is 40° less than the larger angle. Find the angles.

Answer :-

• Let the larger angle be "x".

• Since the smaller angle is 40° less than the larger angle, therefore it will be x - 40°.

• We know that complementary angles add up to 90°.

• So, the sum of x and x - 40° is equal to 90°.

-----------------------------

$\longmapsto\sf x + x - 40^{\circ} = 90^{\circ}$

Adding the variables,

$\longmapsto\sf2x - 40^{\circ} = 90^{\circ}$

Transposing 40 from LHS to RHS, changing it's sign,

$\longmapsto\sf2x = 90^{\circ} + 40^{\circ}$

Adding 40 to 90,

$\longmapsto\sf2x = 130^{\circ}$

Transposing 2 from LHS to RHS, changing it's sign,

$\longmapsto\sf x = \dfrac{130^{\circ}}{2}$

Dividing 130 by 2,

$\longmapsto\overline{\boxed{\sf x = 65^{\circ}}}$

• The value of x is 65°.

-----------------------------

So, the angles are as follows :-

$\bf x = 65^{\circ}$

$\bf x - 40^{\circ} = 65^{\circ} - 40^{\circ} = 25^{\circ}$