Answers:
x = 72
y = 83
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Explanation:
Angle VFG is 50 degrees. The angle adjacent to this is angle EFG which is 180-50 = 130 degrees.
Angle HDW is 77 degrees. The supplementary angle adjacent to this is 180-77 = 103 degrees which is angle EDH.
Pentagon EFGHD has the following five interior angles
- E = x
- F = 130
- G = 170
- H = 65
- D = 103
Note that angles F = 130 and D = 103 were angles EFG and EDH we calculated earlier.
For any pentagon, the interior angles always add to 180(n-2) = 180(5-2) = 180*3 = 540 degrees.
This means,
E+F+G+H+D = 540
x+130+170+65+103 = 540
x+468 = 540
x = 72
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Now focus your attention on triangle THS
We see that the interior angles are
The angle H is 65 degrees because it's paired with the other 65 degree angle shown. They are vertical angles.
For any triangle, the angles always add to 180
T+H+S = 180
y+65+32 = 180
y+97 = 180
y = 180-97
y = 83
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 
, hence
y = - x + c ← is the partial equation
To find c substitute (- 3, - 1) into the partial equation
- 1 = 2 + c ⇒ c = - 1 - 2 = - 3
y = - x - 3 ← is the equation of the line
For number 15 and 16, you just have to find the absolute difference between the two points along the calibration of the protractor.
15. ∠BXC = |B - C| = |140° - 110°| = 30°
16. ∠BXE = |B - E| = |140° - 30°| = 110°
For numbers 20 and 21, apply the Angle Addition Postulate. This is when you add the individual interior angles to equate to the total angle.
20. ∠PQS = ∠PQR + ∠RQS
112° = 72°+ 10x°
x = 4
21. ∠KLM = ∠KLN + ∠NLM
135° = 47°+ 16y°
y = 5.5
