Question

1. The sides of AB and AC of a triangle ABC are produced to D and E respectively such that DBC=125° and BCE=95°, find the value of BAC.
2. In a triangle ABC, BAC= 48° and ABC=100°, calculate the acute angle between the internal bisectors of ABC and BCA.

3. The angles of a quadrilateral are 4x, x+10, 9x-30 and 3x+20. The value of x is..

4. Each of the exterior angle of a regular polygon is 24°. How many sides has the polygon?

5. Each interior angle of an eight-sided polygon is equal to...

6. The interior angles of a pentagon are 130°, 118°, 80°, 78° and x. Find the value of x

7. The ratio of the interior angle to to the exterior angle in a regular polygon is 1.4, what is the number of sides

8. The two adjacent angles on a straight line are(x-60) 0 and (y+30). The value of x+y is

9. Calculate the sum of angles in a regular decagon

10. When two straight lines cross each other, which angle is formed

Answer 1

Answer:

4. Let the number of sides be n

As we know that sum of exterior angles of a regular polygon = 360°

Number of sides = Sum of exterior angles/Each interior angle

= 360°/24°

= 15

Hence, the regular polygon has 15 sides

10. Non-Perpendicular Intersecting Lines

When two lines intersect, they create vertical angles, sometimes called opposite angles, that are congruent.