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In a \( \Large \triangle ABC \), \( \Large \angle A \) : \( \Large \angle B \) : \( \Large \angle C \) = 2 : 3 : 4. A line CD drawn parallel to AB, then \( \Large \angle ACD \) is

A) \( \Large 80 ^{\circ} \)
B) \( \Large 20 ^{\circ} \)
C) \( \Large 40 ^{\circ} \)
D) \( \Large 60 ^{\circ} \)

Correct Answer:



C) \( \Large 40 ^{\circ} \)

Description for Correct answer:

Let the angles be 2x, 3x and 4x.

Then. \( \Large 2x + 3x + 4x = 180 ^{\circ} \)

\( \Large 9x = 180 ^{\circ} => x = 20 ^{\circ} \)

\( \Large \therefore \angle A = 2x = 2 \times 20 = 40 ^{\circ} \)

\( \Large \angle B = 3x = 3 \times 20 = 60 ^{\circ} \)

\( \Large \angle C = 4x = 4 \times 20 = 80 ^{\circ} \)

Now, \( \Large AB \parallel CD\ and\ AC\

be\ the\ transversal. \)

Then, \( \Large \angle BAC = \angle ACD \)

[alternate interior angles]

\( \Large \therefore \angle ACD = 40 ^{\circ} \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

Comments

Similar Questions

1). The mid-points of AB and AC of a \( \Large \triangle ABC \) are respectively X and Y. If BC + XY = 12 units, then the value of BC - XY is

A). 6

B). 8

C). 4

D). 12

2). In the figure given below, \( \Large \angle ABC \) = \( \Large \angle AED \) = \( \Large 90 ^{\circ} \)

Consider the following statements
I. ABC and ADE are similar triangles.
II. The four points B, C, E and D may lie on a circle.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both I and ll

D). Neither I nor ll

3). In a \( \Large \triangle ABC \), \( \Large \angle BCA = 60 ^{\circ} \) and \( \Large B^{2} = BC^{2} + CA^{2} + X \). What is the value of X?

A). \( \Large \left(BC\right) \left(CA\right) \)

B). \( \Large - \left(BC\right) \left(CA\right) \)

C). \( \Large \left(AB\right) \left(BC\right) \)

D). Zero

4). In a \( \Large \triangle ABC \), XY is drawn parallel to BC, cutting sides at X and Y, where AB = 4.8 cm, BC = 7.2 cm and BX = 2 cm. What is the length of XY?

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B). 4.1 cm

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D). 4.3 cm

5). The angles \( \Large x ^{\circ} \), \( \Large a ^{\circ} \), \( \Large c ^{\circ} \) and \( \Large \left( \pi - b\right) ^{\circ} \) are indicated in the figure given below. Which one of the following is correct?

A). x = a + c - b

B). x = b - a - c

C). x = a + b + c

D). x = a - b + c

6). In the figure given below, \( \Large YZ \parallel MN \), \( \Large XY \parallel \ LM \ and \ XZ \parallel LN\) Then, MY is

A). the median of ALMN

B). the angular bisector of ALMN

C). perpendicular to LN

D). perpendicular bisector ol LN

7). In the figure given below, AB is parallel to CD \( \Large AB \parallel CD \), \( \Large \angle ABC \) = \( \Large 65 ^{\circ} \), \( \Large \angle CDE \) = \( \Large 15 ^{\circ} \) and AB = AE. What is the value of \( \Large \angle AEF \)?

A). \( \Large 30 ^{\circ} \)

B). \( \Large 35 ^{\circ} \)

C). \( \Large 40 ^{\circ} \)

D). \( \Large 45 ^{\circ} \)

8). External angle of a regular polygon is \( \Large 72^{\circ} \). Find the sum of all the internal angles of it.

A). \( \Large 360 ^{\circ} \)

B). \( \Large 480 ^{\circ} \)

C). \( \Large 352 ^{\circ} \)

D). \( \Large 540 ^{\circ} \)

9). The ratio of the numbers of sides of two regular polygons is 1 : 2. If each interior angle of the first polygon is \( \Large 120 ^{\circ} \), then the measure of each interior angle of the second polygon is

A). \( \Large 140 ^{\circ} \)

B). \( \Large 135 ^{\circ} \)

C). \( \Large 150 ^{\circ} \)

D). \( \Large 160 ^{\circ} \)

10). In the quadrilateral ABCD shown below, \( \Large \angle \)DAB = \( \Large \angle \)DCX = \( \Large 120 ^{\circ} \). If \( \Large \angle \)ABC = \( \Large 105 ^{\circ} \), then what is the value of \( \Large \angle \)ADC?

A). \( \Large 45 ^{\circ} \)

B). \( \Large 60 ^{\circ} \)

C). \( \Large 75 ^{\circ} \)

D). \( \Large 95 ^{\circ} \)