Answer:
<h2><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>135</u></em><em><u>°</u></em></h2>
Step-by-step explanation:
<em><u>According</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>problem</u></em><em><u>, </u></em>
45° + x = 180° <em>[</em><em>Linear</em><em> </em><em>pair</em><em>]</em>
=> x = 180° - 45°
=> <em><u>x = 135° (Ans)</u></em>
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle.
The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
r² = x² + y²
If we are to simplify this for the r alone, we have,
r = sqrt (x² + y²)
Substituting the known values,
r = sqrt ((4)² + (-4)²) = 4√2
The x and y can be related through the trigonometric function, tangent.
tan θ = y/x
To solve for θ
θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°
Hence, the polar coordinate is <em>(4√2, 315°)</em>
Answer:
72miles
Step-by-step explanation:
The angles of a quadrilateral add to 360, so we can solve for x by adding the 4 angle measures together and setting it equal to 360:
90 + 140 + (x - 10) + (x - 20) = 360
Combine like terms:
230 + 2x - 30 = 360
200 + 2x = 360
200 - (200) + 2x = 360 - (200)
2x = 160
Divide both sides by 2:
2x/(2) = 160/(2)
x = 80
