Question 9 of 15intermediate🔧 ApplyShort Answer4 marks

For each of the following angles, find another angle for which a triangle is (a) possible, (b) not possible. Find at least two different angles for each category: (a) 30° (b) 70° (c) 54° (d) 144°

(a)
Answer

Possible: 40°, 100° (sums 70°, 130° < 180°). Not possible: 160°, 170° (sums 190°, 200° ≥\geq 180°).

(b)
Answer

Possible: 50°, 60° (sums 120°, 130° < 180°). Not possible: 120°, 130° (sums 190°, 200° ≥\geq 180°).

(c)
Answer

Possible: 60°, 80° (sums 114°, 134° < 180°). Not possible: 130°, 140° (sums 184°, 194° ≥\geq 180°).

(d)
Answer

Possible: 20°, 30° (sums 164°, 174° < 180°). Not possible: 40°, 50° (sums 184°, 194° ≥\geq 180°).

Explanation

(a) Triangle exists when sum with 30° is less than 180°. (b) Triangle exists when sum with 70° is less than 180°. (c) Triangle exists when sum with 54° is less than 180°. (d) Triangle exists when sum with 144° is less than 180°.

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