What is the value of x? to x = [?]° o

Mathematics

1 answer:

Ugo [173]2 years ago

6 0

Answer:

The value of x from the figure is 58 degrees

To get the value of x, we will use the formula:

The angle at the vertex = 1/2(difference of angles at the arc)

Angle at the vertex = 1/2(160 - x)

51 = 1/2(160 - x)

102 = 160 - x

x = 160 - 102

x = 58 degrees

Hence the value of x from the figure is 58 degrees

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What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?

Sati [7]

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The coordinates of the orthocenter of △JKL is (-4, 8)

Solution-

The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.

For a right angle triangle, the vertex at the right angle is the orthocentre of the triangle.

Here we are given the three vertices of the triangle are J(-4,-1), K(-4,8) and L(2,8)

If the triangle JKL satisfies Pythagoras Theorem, then triangle JKL will be a right angle triangle.

Applying distance formula we get,

$JK^2= (-4+4)^2+ (8+1)^2=0+81=81\\\\KL^2= (-4-2)^2+ (8-8)^2=36+0=36\\\\JL^2= (-4-2)^2+(8+1)^2=36+81=117$