Question

ll. If(a-27)°and (2a+15)° are complementary, then find a
12​

Answer 1

Given:-

• Two complementary angles are (a - 27)° and (2a + 15)°.

To find:-

• Value of a.

Solution:-

We know that,

Sum of two complementary angles is 90°

So,

$\implies \sf \: (a - 27)\degree + (2a + 15)\degree = 90\degree$

$\implies \sf \: a - 27\degree + 2a + 15\degree =90 \degree$

$\implies \sf \: a + 2a - 27\degree + 15\degree = 90\degree$

$\implies \sf \: 3a - 12\degree = 90\degree$

$\implies \sf \: 3a = 90 \degree +12 \degree$

$\implies \sf \: 3a = 102\degree$

$\implies \sf \: a = \frac{108\degree}{3}$

$\implies \sf \: a = 34 \degree$

Verification:-

$\implies \sf \: (a - 27)\degree + (2a + 15)\degree = 90\degree$

$\implies \sf \: a - 27\degree + 2a + 15\degree = 90\degree$

• Put a = 34°

$\implies \sf \: 34\degree - 27\degree + (2 \times 34\degree ) + 15\degree = 90\degree$

$\implies \sf \: 7 \degree + 68\degree + 15\degree = 90\degree$

$\implies \sf \: 90\degree = 90\degree$

Therefore,

Value of a is 34°.