Grade 10 Maths · Euclidean Geometry

Use angle sum of a triangle

Find a missing angle in a triangle because the three angles add up to 180° (for example 50° + 60° + x = 180°, so x = 70°).

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Finding the Missing Angle of a Triangle: A Step-by-Step GuideMath with Mr. J

Gr 9 Geometry: Lines and TrianglesKevinmathscience

How To Calculate The Missing Angle In a TriangleThe Organic Chemistry Tutor

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Question 6.1 · November 2024 · Paper 2 · Provincial · 2 marks

An observer on the top of a cliff, 200 m above the sea level, observes the angles of depression of the two ships to be

4 5^{\circ}

for ship A, and

3 0^{\circ}

for ship B. Diagram for this question

6.1 Determine the size of

B \hat{D} C

.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: use angle sum of a triangle

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3. Question 4.2.2 · March 2022 · Provincial · 2 marks
4.2 EFGH is a rhombus in which the diagonals EG and FH intersect at M. $F \hat{E} H = 10 0^{\circ}$ . Find the value of:
4.2.2 $E \hat{F} M$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Equation with reason (R) $E \hat{F} M = 18 0^{\circ} - (5 0^{\circ} + 9 0^{\circ})$ (sum of $∠$ s in $Δ$ )
  1 mark · Use angle sum of a triangle
2. ✓
  Answer (S) $E \hat{F} M = 4 0^{\circ}$
  1 mark · Use angle sum of a triangle
4. Question 5.1.2 · March 2020 · Provincial · 2 marks
5.1 In the figure, BCDE is a cyclic quadrilateral. $BC // E D$ in the circle with centre A. BE and CD produced meet at F. $\hat{D}_{3} = x$ .
5.2 B is the centre of the larger circle CEFG. BC is the diameter of the smaller circle CDB. HC is a tangent to both circles at C. $G H ⊥ H C$ and $\hat{C}_{1} = x$ .
5.1.2 If $∠ D_{3} = x$ , determine the value of $\hat{F}$ , in terms of x.(2)
Show the memo (2 ticks)Memo
1. ✓
  Statement $\hat{F} = 18 0^{\circ} - 2 x$
  1 mark · Use angle sum of a triangle
2. ✓
  Reasonsum of $∠$ s in $Δ FE D$
  1 mark · Use angle sum of a triangle
5. Question 4.1.2(d) · March 2020 · Provincial · 2 marks
In the diagram below, points A, B, C and D lie on the circumference of a circle. FG and FD are tangents to the circle at C and D respectively. CD is produced to meet AE at E. Furthermore, $∠ GC A = 7 8^{\circ}$ , $∠ CB D = 4 1^{\circ}$ and $∠ B D A = 3 4^{\circ}$ .
4.1.2 Determine with reasons the sizes of the following angles:
4.1.2(d) $\hat{F}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement and reason $\hat{F} + 4 1^{\circ} + 4 1^{\circ} = 18 0^{\circ}$ (int $∠$ s of $Δ FC D$ )
  1 mark · Use angle sum of a triangle
2. ✓
  Answer $\hat{F} = 9 8^{\circ}$
  1 mark · Use angle sum of a triangle
6. Question 5.2.3 · March 2020 · Provincial · 2 marks
5.2 AE is a diameter of the circle. AE is produced to D. DB is a tangent to the circle at B. DC is perpendicular to AD. CBA is a straight line. BE and EC are drawn. Let $\hat{A} = x .$
5.2.3 Prove that $\hat{E}_{1} = \hat{E}_{3}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Express E1 in terms of x $\hat{E}_{1} = 18 0^{\circ} - (\hat{A} + \hat{B}_{3})$ (sum of $∠$ s of $Δ$ ABE)
  $= 18 0^{\circ} - (x + 9 0^{\circ}) = 9 0^{\circ} - x$
  1 mark · Use angle sum of a triangle
2. ✓
  Express E3 in terms of x $\hat{E}_{3} = 18 0^{\circ} - (\hat{C}_{1} + C \hat{D} E)$ (sum of $∠$ s of $Δ$ CDE)
  $= 18 0^{\circ} - (x + 9 0^{\circ}) = 9 0^{\circ} - x$
  $∴ \hat{E}_{1} = \hat{E}_{3}$
  1 mark · Use angle sum of a triangle

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