What is the measure of x?
2 answers:
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Answer:
Step-by-step explanation:
The complete question in the attached figure
we know that
When two lines are crossed by another line (transversal), a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal, are called <em><u>Alternate Interior Angles</u></em>.
When the two lines being crossed are Parallel Lines the Alternate Interior Angles are congruent
In this problem
---> by alternate interior angles
we have
therefore
Let's assume,
Hence, the given equation can be written as:
y² - y - 6 = 0
Next step is to factor the trinomial. For that, break down the constant -6 into two multiples so that their addition will result the coefficient of y =-1.
So, 6 = -3* 2
And sum of -3 and 2 will give -1.
Therefore, we can replace -y with -3y + 2y. So,
y² - 3y + 2y - 6 =0
(y² - 3y) + (2y - 6) =0 Make the group of terms.
y(y - 3)+ 2(y -3) =0 Take out the common factor from each group.
(y - 3 ) (y + 2) = 0 Take out the common factor (y - 3).
So, y - 3 = 0 and y + 2 =0 Equate both factor equal to 0.
Hence, y = 3 and -2.
So,
Taking ln to each sides.
So, x = ln 3
But ln (-2) is not defined.
So, x = ln (3) is the real solution of the given equation.
Therefore the point P is at 3.46 cm from O and it lies on the angle bisector of ∠XOY
<h3>What is an Angle Bisector ?</h3>The ray that bisects the angle into half is called Angle Bisector.
It is given that ∠XOY = 60 degree
the length of OX = 4.5 cm
OY =5 cm
The point M is on OX such that
OM = 2 MX
so The M is at 3 cm from O
The point P lies in the acute angle such that the distance between point P and OX and OY is always same and at 3 cm from M
According to the angle bisector theorem converse states that if a point is in the interior of an angle and is at equal distance from the sides then it lies on the bisector of that angle.
As it can be seen from the image that a point equidistant from the rays , at 3 cm from M will be at
By Pythagoras Theorem
3² +3² = OP²
OP = 2 = 3.46 cm from O
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