Geometry & Mensuration • Topic 1 of 5

Lines & Angles

When two lines meet, vertically opposite angles are equal and a linear pair sums to 180 degrees. With a transversal across parallel lines, corresponding and alternate angles are equal and co-interior angles sum to 180. Angles around a point sum to 360. These rules, plus the triangle angle sum, settle most figure-chasing questions.

✅ Solved examples

1. Two angles are complementary and one is 35 degrees. The other?
Complementary sum 90; 90 - 35 = 55 degrees.
2. Two angles on a straight line; one is 110 degrees. The other?
Linear pair sums 180; 180 - 110 = 70 degrees.
3. Parallel lines cut by a transversal; one alternate angle is 65 degrees. Its pair?
Alternate angles are equal: 65 degrees.
4. Three angles around a point are 120, 150 and x. Find x.
Sum 360; x = 360 - 270 = 90 degrees.

✏️ Practice — try these, take hints as needed

1. Supplement of 75 degrees?
Sum 180.
180 - 75.
—
105 degrees
2. Complement of 40 degrees?
Sum 90.
90 - 40.
—
50 degrees
3. Co-interior angle to 70 (parallel lines)?
Sum 180.
180 - 70.
—
110 degrees
4. Angles around a point: 100, 130, x?
Sum 360.
360 - 230.
—
130 degrees
5. Vertically opposite to 55 degrees?
Equal.
—
—
55 degrees

📝 Topic test — 8 questions

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