If two angles of a triangle are x° and y° with y = 4x, and the third angle is 50°, what are the angles?
Answer: x = 26°, y = 104°; the angles are 26°, 104° and 50°.
Step-by-step solution
Idea: Angle sum of a triangle = 180° gives one equation; y = 4x is the second. Since y is already expressed in terms of x, substitution is natural.
- Angle sum property: x + y + 50 = 180 … (1). Given y = 4x … (2).1 mark
- Substitute (2) in (1): x + 4x + 50 = 180 ⇒ 5x = 130 ⇒ x = 26.1 mark
- y = 4 × 26 = 104. The angles are 26°, 104° and 50°.1 mark
The angles are 26°, 104° and 50°.
Check: 26 + 104 + 50 = 180 ✓ and 104 = 4 × 26 ✓.
Answer to write in the exam
x + y + 50 = 180 (angle sum property) … (1)
y = 4x … (2)
(2) in (1): 5x + 50 = 180 ⇒ x = 26
y = 4 × 26 = 104
∴ Angles: 26°, 104°, 50°
Common mistakes that cost marks
- Forgetting the 50° and solving x + 4x = 180 (gives 36°).
- Stopping at x = 26 and not finding y.
How this can come in the exam
MCQ (1 mark)
In a triangle, one angle is 40° and the other two are p° and q° with q = 2p + 5. Then p =
- 45
- 45⅓
- 40
- 35
Show answer
(A) 45
p + 2p + 5 + 40 = 180 ⇒ 3p = 135 ⇒ p = 45.
Try one yourself
Two angles of a triangle are a° and b° with b = a + 30, and the third is 70°. Find a and b.
Show answer
2a + 100 = 180 ⇒ a = 40°, b = 70°.
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