Question

the sum of an angle and half of its complementary angle is 75 degrees. find the angle

Answer 1

Solution:

The complementary angles are the angles which add upto 90°. Their sum is 90°. So, here we have an angle and half of its complementary which sums up to 75°

Let,

• The angle be x.
• Then it's complementary angle will be (90 - x)°

According to question,

➝ $\sf{ x + \dfrac{(90 - x) \degree}{2} = 75 \degree}$

Now taking the LCM in LHS and proceed...

➝ $\sf{ \dfrac{2x + 90 - x}{2} = 75 \degree}$

➝ $\sf{\dfrac{90 + x}{2} = 75 \degree}$

Cross multiplying,

➝ $\sf{90 \degree + x = 150 \degree}$

Then, our required angle x = 60° (Answer)

And we are done !

Answer 2

Answer:

The required angle is 60° .

Step-by-step explanation:

Let the required angle be x.

• COMPLEMENTARY ANGLES

Two Angles are Complementary when they add up to 90° .

Complement of an angle = 90° - Given Angle

Complement of x = 90° - x

Half the complement of x = $\frac{1}{2} (90 ^ \circ - x)$

Half the complement of x = $\frac{(90 ^\circ - x)}{{2} }$

According to Question ,

$x + \frac{(90 ^\circ - x)}{{2} } = 75 {}^ \circ \\ \\ \implies \: \frac{x}{1} + \frac{(90 ^\circ - x)}{{2} } = 75 {}^ \circ \\ \\ \implies \frac{2x + 90 ^ \circ \: - x}{2} = 75 ^ \circ \\ \\ \implies \: \frac{x + 90 ^ \circ }{2} = 75 ^ \circ \\ \\ \implies \: x + 90 ^ \circ = 2 \times 75 ^ \circ \\ \\ \implies \: x + 90 ^ \circ = 150 ^ \circ \\ \\ \implies \: x = 150 ^ \circ - 90 ^ \circ \\ \\ \implies \: x = 60 ^ \circ$

Therefore , the required angle is 60°.

DONE ✅

HOPE IT HELPS YOU !

THANKS !