Question

Qm. 4 If an angle is 30° more than one half of its complement, find the of the angle measure​

Answer 1

50°

Explanation:

Complementary angles are a pair of angles that sum to 90°.

Therefore, the complement of an angle is 90° minus the angle itself.

Let x be the measure of the angle in degrees.

So, the complement of x is (90° - x).

According to the problem statement, the angle is 30° more than one-half of its complement. Mathematically, this can be expressed as:

`x = (1)/(2)(90^(\circ) - x) + 30^(\circ)`

To solve for x, begin by multiplying both sides of the equation by 2 to eliminate the fraction:

`2x = 90^(\circ) - x + 60^(\circ)`

Combine like terms:

`2x = 150^(\circ) - x`

Add x to both sides of the equation:

`3x = 150^(\circ)`

Now, divide by 3 to find the value of x:

`x = (150^(\circ))/(3) = 50^(\circ)`

So, the measure of the angle is 50°.