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
[tex]mHMK=\frac{1}{2}(mJL+mHLK)[/tex]
On putting the values in the above formula, we get
⇒ [tex](8x-1)=\frac{1}{2}(15x-36+3x+2)[/tex]
On applying cross-multiplication, we get
⇒ [tex]2(8x-1)=18x-34[/tex]
⇒ [tex]16x-2=18x-34[/tex]
On subtracting "18x" from both sides, we get
⇒ [tex]16x-2-18x=18x-34-18x[/tex]
⇒ [tex]-2x-2=-34[/tex]
On adding "2" both sides, we get
⇒ [tex]-2x=-34+2[/tex]
⇒ [tex]-2x=-32[/tex]
⇒ [tex]x=\frac{32}{2}[/tex]
⇒ [tex]x=16[/tex]
On putting the value of "x" in mHLK = (15x-36)°, we get
⇒ (15x-36)° = (15×16-36)°
⇒ = (240-36)°
⇒ = (204)°
So that mHLK = (204)°
