Answer:
1. ∠1 = 120°
2. ∠2 = 60°
3. ∠3 = 60°
4. ∠4 = 60°
5. ∠5 = 75°
6. ∠6 = 45°
Step-by-step explanation:
From the diagram, we have;
1. ∠1 and the 120° angle are corresponding angles
Corresponding angles are equal, therefore;
∠1 = 120°
2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;
∠2 + 120° = 180°
∠2 = 180° - 120° = 60°
∠2 = 60°
3. Angle ∠3 and ∠2 are vertically opposite angles
Vertically opposite angles are equal, therefore, we get;
∠3 = ∠2 = 60°
∠3 = 60°
4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;
∠1 + ∠4 = 180°
∠4 = 180° - ∠1
We have, ∠1 = 120°
∴ ∠4 = 180° - 120° = 60°
∠4 = 60°
5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6
Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;
x = y
The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles
∴ x + y + 90° = 180°
From x = y, we get;
y + y + 90° = 180°
2·y = 180° - 90° = 90°
y = 90°/2 = 45°
y = 45°
Therefore, we have;
∠4 + ∠5 + y = 180° (Angle sum property of a triangle)
∴ ∠5 = 180 - ∠4 - y
∠5 = 180° - 60° - 45° = 75°
∠5 = 75°
6. ∠6 and y are alternate angles, therefore;
∠6 = y = 45°
∠6 = 45°.
Answer:
B option is right
Step-by-step explanation:
These 3 will form a 3d system.
Answer:
That is a Multi Step Equation
Solve for x for x: x+2y=2
x+2y +-2y=2+-2y (add -2y on both sides.)
x=-2y+2
Substitute : -2y+2 for x in
4x-y=4:
4(-2y+2)-y=4
-9y+8=4 Simplify both sides of the equation.
-9y+8+-8=4+-8 Add -8 to both sides.
-9y=-4
-9/-9=-4-9 Divide both sides by -9
y=4/9
Substitute 4/9 for y in
x=-2y+2
x=-2(4/9)+2
x=10/9
y=4/9,x=10/9
1. 20 of 40 is 50% 20/40 = 1/2 1/2 = 50%
2. It is 20% because 600 is 20% of 3000
3. 40% of 30 = 12 50 = 15 10% = 3 (get it)
4, 40% of 65 = 26 50%= 32.5 (get it)