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1 day ago

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

Mathematics

1 answer:

lawyer [4K]1 day ago

4 0

Response:

The measure of mHLK is "(204)°".

Step-by-step breakdown:

Given values include:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

What is mHLK?

Now,

Utilizing the chord-chord angle formula, we find

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

Inserting the known values into the equation gives us

⇒ $(8x-1)=\frac{1}{2}(15x-36+3x+2)$

By carrying out cross-multiplication, we arrive at

⇒ $2(8x-1)=18x-34$

⇒ $16x-2=18x-34$

By subtracting "18x" from both sides, we obtain

⇒ $16x-2-18x=18x-34-18x$

⇒ $-2x-2=-34$

Upon adding "2" to both sides, we end up with

⇒ $-2x=-34+2$

⇒ $-2x=-32$

⇒ $x=\frac{32}{2}$

⇒ $x=16$

By substituting the value of "x" into mHLK = (15x-36)°, we calculate

⇒ (15x-36)° = (15×16-36)°

⇒ = (240-36)°

⇒ = (204)°

Thus, mHLK = (204)°

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