Sasi Math (Revised for 1024)

Scroll:Geometry >> Triangles >> ps (1559)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

31°

107°

16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 31°.

Find ∠ DFE.

Answer:_______________

37°

119°

22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 37°.

Find ∠ DFE.

Answer:_______________

39°

120°

21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 39°.

Find ∠ DFE.

Answer:_______________

36°

117°

21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 36°.

Find ∠ DFE.

Answer:_______________

35°

115°

20°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 20° and∠ ABD = 35°.

Find ∠ DFE.

Answer:_______________

36°

118°

22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 36°.

Find ∠ DFE.

Answer:_______________

36°

115°

19°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 19° and∠ ABD = 36°.

Find ∠ DFE.

Answer:_______________

33°

110°

17°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 17° and∠ ABD = 33°.

Find ∠ DFE.

Answer:_______________

39°

116°

17°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 17° and∠ ABD = 39°.

Find ∠ DFE.

Answer:_______________

10)

34°

109°

15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 34°.

Find ∠ DFE.

Answer:_______________

31°

107°

16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 31°.

Find ∠ DFE.

Answer: 107^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 31 ^o = 29^o

Step 3: ∠ FCB = 60^o - 16 ^o = 44^o

Step 4: ∠ BFC = 180^o - 29 ^o - 44 ^o = 107^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 107^o (vertically opposite angles)

37°

119°

22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 37°.

Find ∠ DFE.

Answer: 119^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 37 ^o = 23^o

Step 3: ∠ FCB = 60^o - 22 ^o = 38^o

Step 4: ∠ BFC = 180^o - 23 ^o - 38 ^o = 119^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 119^o (vertically opposite angles)

39°

120°

21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 39°.

Find ∠ DFE.

Answer: 120^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 39 ^o = 21^o

Step 3: ∠ FCB = 60^o - 21 ^o = 39^o

Step 4: ∠ BFC = 180^o - 21 ^o - 39 ^o = 120^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 120^o (vertically opposite angles)

36°

117°

21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 36°.

Find ∠ DFE.

Answer: 117^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 36 ^o = 24^o

Step 3: ∠ FCB = 60^o - 21 ^o = 39^o

Step 4: ∠ BFC = 180^o - 24 ^o - 39 ^o = 117^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 117^o (vertically opposite angles)

35°

115°

20°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 20° and∠ ABD = 35°.

Find ∠ DFE.

Answer: 115^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 35 ^o = 25^o

Step 3: ∠ FCB = 60^o - 20 ^o = 40^o

Step 4: ∠ BFC = 180^o - 25 ^o - 40 ^o = 115^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 115^o (vertically opposite angles)

36°

118°

22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 36°.

Find ∠ DFE.

Answer: 118^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 36 ^o = 24^o

Step 3: ∠ FCB = 60^o - 22 ^o = 38^o

Step 4: ∠ BFC = 180^o - 24 ^o - 38 ^o = 118^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 118^o (vertically opposite angles)

36°

115°

19°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 19° and∠ ABD = 36°.

Find ∠ DFE.

Answer: 115^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 36 ^o = 24^o

Step 3: ∠ FCB = 60^o - 19 ^o = 41^o

Step 4: ∠ BFC = 180^o - 24 ^o - 41 ^o = 115^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 115^o (vertically opposite angles)

33°

110°

17°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 17° and∠ ABD = 33°.

Find ∠ DFE.

Answer: 110^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 33 ^o = 27^o

Step 3: ∠ FCB = 60^o - 17 ^o = 43^o

Step 4: ∠ BFC = 180^o - 27 ^o - 43 ^o = 110^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 110^o (vertically opposite angles)

39°

116°

17°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 17° and∠ ABD = 39°.

Find ∠ DFE.

Answer: 116^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 39 ^o = 21^o

Step 3: ∠ FCB = 60^o - 17 ^o = 43^o

Step 4: ∠ BFC = 180^o - 21 ^o - 43 ^o = 116^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 116^o (vertically opposite angles)

10)

34°

109°

15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 34°.

Find ∠ DFE.

Answer: 109^o

SOLUTION 1 :

Step 1: ∠ ABC = ∠ ACB = 60^o (equilateral triangle)

Step 2: ∠ FBC = 60^o - 34 ^o = 26^o

Step 3: ∠ FCB = 60^o - 15 ^o = 45^o

Step 4: ∠ BFC = 180^o - 26 ^o - 45 ^o = 109^o (sum of angles in a triangle)

Step 5: ∠ DFE = ∠ BFC = 109^o (vertically opposite angles)