Find the angel x in d diagram above with a well structured solution.Thanks
1 answer:
Step-by-step answer:
Please refer to attached image.
1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning
that
angles QPS and QRS are supplementary =>
QPS+QRS=180 =>
QRS = 180 - 74 = 106
2. Triangle RSQ is isosceles with RS=RQ =>
angles RSQ and RQS are congruent.
3. Angle RSQ = (180 - 106) /2 = 74 / 2 = 37
4. QP is a diameter => angle QSP is a right-angle.
5. From (3) and (4) above,
angle RSP = 37+90 = 127
6. Since PQRS is cyclic, angles RQP and RSP are supplementary =>
RQP+RSP = 180 =>
x + 127 = 180 =>
x = 180 - 127 = 53 degrees.
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<u>Factoring:</u>
This equation cannot be factored because its roots are irrational (as shown by solving with the quadratic formula). Also, to factor a quadratic equation, you need to find a pair of numbers whose product is equal to the c term (-5) and whose sum is equal to the b term (-6). There is no pair of numbers which satisfies this, further showing that the equation cannot be factored.
<u>Quadratic Formula:</u>
The quadratic formula is x=.
First, you need to find the a, b and c terms of your equation. They are 1, -6, and -5 respectively.
Now, you must plug in to the equation and solve for x. You must do so twice, once with a plus sign in the numerator and once with a minus.
The answers are 3+√14 and 3-√14.
Hope this helps!!