Diagram shows an irregular hexagon PQRSTU.Fine the value of X + Y=
1 answer:
To find the value of x+y, we will first find the sum of all the interior angles of the hexagon.The sum of the interior angles in a hexagon is always equal to 720 degrees.
All the angles in the diagram are in terms of x or y except for angle t. However, we know that the corresponding exterior angle is 30 degrees. The sum of angle t and 30 is 360. We can solve this in an algebraic equation.
t+30=360
Subtract 30 from both sides
t = 330
Now, we can solve for the values of x+y. We can set this up in another algebraic equation.
x+x+x+2y+y+30=720
Combine like terms:
3x+3y+30 = 720
Subtract 30 from both sides:
3x+3y = 690
Divide both sides by 3:
x+y = 230
The sum of x and y is 230.
All the angles in the diagram are in terms of x or y except for angle t. However, we know that the corresponding exterior angle is 30 degrees. The sum of angle t and 30 is 360. We can solve this in an algebraic equation.
t+30=360
Subtract 30 from both sides
t = 330
Now, we can solve for the values of x+y. We can set this up in another algebraic equation.
x+x+x+2y+y+30=720
Combine like terms:
3x+3y+30 = 720
Subtract 30 from both sides:
3x+3y = 690
Divide both sides by 3:
x+y = 230
The sum of x and y is 230.
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Angle B measures 30 degrees.
Step-by-step explanation:
Step 1:
If two angles are complementary, the sum of the two angles will equal 90°.
So if angles A and B are complementary, the sum of the angles A and B will equal 90°.
It is given that cos A = 0.5, we can determine the value of A by taking the cos inverse of the value 0.5.
Step 2:
If cos A = 0.5, A = So angle A is 60°.
As A and B are complementary, angle A + angle B = 90°.
So 60° + angle B = 90°, angle B = 90° - 60° = 30°.
So angle B measures 30° while angle A measures 60°.