ABCD is a quadrilateral. Sides are extended as shown. Show that x = 100°
1 answer:
Solution :
Given :
ABCD is a quadrilateral.
Angle ADC = 90 degree
Angle DCB = 120 degree
Now angle DAB = 70 degree (alternate angles)
We know that the interior angles of a quadrilateral is 360 degrees.
So,
∠ DAB + ∠ ABC + ∠ BCD + ∠ CDA = 360°
70° + ∠ ABC + 120° + 90 ° = 360°
∠ ABC = 360° - (70° + 120° + 90°)
∠ ABC = 360° - 280°
∠ ABC = 80°
Now ∠ x = 180° - ∠ ABC (Line AB extended is 180° )
= 180° - 80°
= 100°
Hence proved.
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Answer:
A) x = {5, 7}
B) The solutions make the equation true.
Step-by-step explanation:
<u>Part A</u>:
To solve this by factoring, you need to find factors of 35 that have a sum of -12. Since 35 is the product of two primes, the search is a short one.
35 = (-1)(-35) = (-5)(-7)
The corresponding sums are -36 and -12, so the latter factor pair is the one we want. Since the coefficient of x^2 is 1, we can use these numbers directly in the binomial factors:
x^2 -12x +35 = (x -5)(x -7) = 0
The zero product rule tells us this product is zero only when one of the factors is zero:
x -5 = 0 ⇒ x = 5
x -7 = 0 ⇒ x = 7
The two solutions are x=5 and x=7.
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<u>Part B</u>:
The solutions from part A are the x-intercepts of the graph of the quadratic expression. They are the values of x that make the quadratic expression be zero. That is, they are the values of x that make the equation true.
This is the graph that the equation shows:
