1. a) To construct an angle of 30°:
- Draw a ray AB.
- With A as center and any convenient radius, draw an arc intersecting AB at point P.
- With P as center and the same radius, draw another arc intersecting the first arc at Q.
- With Q as center and the same radius, draw an arc intersecting the first arc at R.
- Bisect angle RAQ by drawing arcs from Q and R with equal radii to find their intersection S.
- Draw ray AS. Angle BAS is 30°.
b) To construct an angle of 45°:
- Draw a ray AB.
- Construct a perpendicular to AB at A to form a 90° angle (using standard perpendicular construction).
- Bisect the 90° angle to obtain two 45° angles.
- The bisector ray forms a 45° angle with AB.
c) To construct an angle of 60°:
- Draw a ray AB.
- With A as center and any convenient radius, draw an arc intersecting AB at P.
- With P as center and the same radius, draw an arc intersecting the first arc at Q.
- Draw ray AQ. Angle BAQ is 60°.
d) To construct an angle of 90°:
- Draw a ray AB.
- With A as center and any convenient radius, draw an arc intersecting AB at P.
- With P as center and the same radius, draw an arc intersecting the first arc at Q.
- With Q as center and the same radius, draw an arc intersecting the first arc at R.
- With Q and R as centers, draw arcs with equal radii intersecting at S.
- Draw ray AS. Angle BAS is 90°.
Parent Tip: Review the logic above to help your child master the concept of geometry 9th grade worksheet.
