Question

If mJI = (3x+2)°, mHLK = (15x-36)°, and m∠HML = (8x-1)°, find mHLK

Answer 1

Answer:

The value of mHLK will be "(204)°".

Step-by-step explanation:

The given values are:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

mHLK = ?

Now,

By using chord-chord formula of angle, we get

$mHMK=\frac{1}{2}(mJL+mHLK)$

On putting the values in the above formula, we get

⇒  $(8x-1)=\frac{1}{2}(15x-36+3x+2)$

On applying cross-multiplication, we get

⇒  $2(8x-1)=18x-34$

⇒  $16x-2=18x-34$

On subtracting "18x" from both sides, we get

⇒  $16x-2-18x=18x-34-18x$

⇒  $-2x-2=-34$

On adding "2" both sides, we get

⇒  $-2x=-34+2$

⇒  $-2x=-32$

⇒  $x=\frac{32}{2}$

⇒  $x=16$

On putting the value of "x" in mHLK = (15x-36)°, we get

⇒ (15x-36)° = (15×16-36)°

⇒                = (240-36)°

⇒                = (204)°

So that mHLK = (204)°