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1 answer:
Answer: The correct answer is option B: The vertical angle
Step-by-step explanation: Please refer to the picture attached for further details.
The circle with center O has an arc AB with a central angle of 42 degrees as shown in the diagram (not draw to scale).
If the line A is extended to point D and also line B is extended to point C both along the circumference of the circle O, then you would have another arc CD on the circle.
If two intersecting lines AD and BC form a pair of angles (shown here as 42° and x°) the angles are called vertical angles, and vertical angles in a circle are equal.
Hence the only thing that can be shown to measure 42 degrees in the question above is a vertical angle.
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Answer:
x = 5
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = bh ( b is the base and h is height )
Here A = 20, b = (x + 3) and h = (2x - 5) , then
(x + 3)(2x - 5) = 20 ← multiply both sides by 2
(x + 3)(2x - 5) = 40 ← expand left side using FOIL
2x² + x - 15 = 40 ( subtract 40 from both sides )
2x² + x - 55 = 0 ← in standard form
(x - 5)(2x + 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - 5.5
But x > 0 , so x = 5