Начертить углы АВС=120° и DBC=45° с общей стороной БС так,чтобы они лежали по одну сторону от неё.Найдите угол ABD

To draw angles ABC = 120° and DBC = 45° with a common side BC, we can follow these steps:

1. Draw a line segment BC as the common side.
2. Place the center of your compass at point B and draw an arc that intersects line BC.
3. Without changing the compass width, move the center of your compass to point C and draw another arc that intersects the previous arc.
4. Label the intersection of the two arcs as point A.
5. Now, place the center of your compass at point B and draw an arc that intersects line BC.
6. Without changing the compass width, move the center of your compass to point C and draw another arc that intersects the previous arc.
7. Label the intersection of the two arcs as point D.
8. Connect points A and D to point B.
9. Lastly, label the angle ABD.

To find the angle ABD, we need to consider the angles formed.

We know that angle DBC = 45°.

Since angles ABC and DBC are linear (they lie on a straight line), the sum of these two angles is 180°.

Therefore, angle ABC = 180° - angle DBC = 180° - 45° = 135°.

To find angle ABD, we can subtract angle DBC from angle ABC:

Angle ABD = angle ABC - angle DBC = 135° - 45° = 90°.

Therefore, angle ABD is equal to 90°.