Question

⑥The difference between the measure of two complementary angle is 160

. The measure of

two angles is

a) 420
,580

b) 370
,530

c) 52
0
,680

d) 400
,560​

Answer 1

$580 - 420 = 160$

$530 - 370 = 160$

$680 - 520 = 160$

$560 - 400 = 160$

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Answer 2

Solution :-

we know that,

• sum of two complementary angles is equal to 90° .

so, let us assume that, the given two complementary angles are x and y , where x > y .

then,

→ x + y = 90° -------- Eqn.(1)

→ x - y = 160° ------- Eqn.(2) (given)

adding Eqn.(1) and Eqn.(2)

→ x + y + x - y = 90° + 160°

→ 2x = 250°

→ x = 125°

putting value of x in Eqn.(1),

→ 125° + y = 90°

→ y = 90° - 125°

→ y = (-35)°

Hence, The measure of two angles is equal to 125° and (-35°) .

Question 2) :- The difference between the measure of two complementary angle is 16° . The measure of two angles is

a) 42° , 58°

b) 37° , 53°

c) 52° , 68°

d) 40° , 56°

Solution :-

let us assume that, the given two complementary angles are x and y , where x > y .

then,

→ x + y = 90° -------- Eqn.(1)

→ x - y = 16° ------- Eqn.(2) (given)

adding Eqn.(1) and Eqn.(2)

→ x + y + x - y = 90° + 16°

→ 2x = 106°

→ x = 53°

putting value of x in Eqn.(1),

→ 53° + y = 90°

→ y = 90° - 53°

→ y = 37°

therefore, option (b) is correct answer .

Hence, The measure of two angles is equal to 37° and 53° .

Shortcut :- Check options , sum of complementary angles must be 90°

a) 42° + 58° = 100° ≠ 90°

b) 37° , 53° = 90°

c) 52° , 68° = 120° ≠ 90°

d) 40° , 56° = 96° ≠ 90° .

therefore, option (b) is correct answer .

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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