Bissoy.com
Doctors Medicines MCQs Q&A

If ABCDE is a regular pentagon, find the value of (y + z - x).

If ABCDE is a regular pentagon, find the value of (y + z - x). Correct Answer 36°

Calculation:

/n

⇒ Angle of a pentagon = /5 = 108°

In a triangle ABE,

⇒ ∠ABE = ∠AEB (∵ AE = AB)

⇒ ∠BAE = 108°

⇒ ∠BAE + ∠ABE + ∠AEB = 180°

⇒ 108° + 2∠AEB = 180°

⇒ ∠AEB = 36° = y

⇒ Δ ABE ≅ Δ BCD

⇒ ∠CBD = 36°

⇒ ∠BDC = z = 36°

⇒ ∠ABC = ∠ABE + ∠DBE + ∠CBD

⇒ 108° = 36° + x + 36°

⇒ x = 36°

⇒ y + z - x = 36° + 36° - 36° = 36°

∴ Required answer is 36°.

Related Questions

Which of the following statements about Regular Expression is/are incorrect? A. The union of two regular expressions is also a regular expression B. The concatenation of two regular expressions is also a regular expression C. The iteration of a regular expression is also a regular expression
Steps given are to draw an involute of a given pentagon ABCDE. Arrange the steps. i. B as centre and radius AB, draw an arc cutting BC –extended at 1. ii. The curve thus obtained is the involute of the pentagon. iii. C as centre and radius C1, draw an arc cutting CD extended at 2. iv. Similarly, D, E, A as centres and radius D2, E3, A4, draw arcs cutting DE, EA, AB at 3, 4, 5 respectively.
ABCDE is a regular pentagon. Its sides are extended as shown in the figure. The value of \(\frac {\angle ABC + 2\angle EGD + 3\angle BAJ}{6}\) is:
In a regular pentagon ABCDE, ratio of area of ΔACD and area of ΔAED.
ABCDE is a regular pentagon. The sides BC and ED are produced to meet at point F and the sides AB and DC are produced to meet at point G. Then, what is the measure of (∠CFD + ∠BGC)?
In the figure given below ABCDEFGH is a regular octagon, if the area of ∆AOH is 36 cm2, then what will be the area of pentagon ABCDE?
In the following question, ABCDE and HIJKL are regular pentagons and AEFGHL is a regular hexagon. If ∠LKB = ∠ABK, then, what is the value of ∠ABK?
Two of the vertices of a regular pentagon drawn on the co-ordinate plane are (11, 17), (23, 22). What is the maximum possible area of such a pentagon?
In the following figure, a regular hexagon, a regular pentagon and an equilateral triangle given, then, find the value of ∠GCH?
A manufacturing company produces 5 types of chairs in two sizes - Regular" and "Large". The pie charts represent the total number of five types of chairs produced and the table shows the ratio between the number of regular sized and large sized chairs of five types. Type of Chair A B C D E Ration between Number of Regular Size and Large Size Chairs 3 : 2 4 : 5 3 : 1 5 : 3 3 : 8   If the total number of all types of chairs produced is 7200, what is the total number of regular size chairs of all types produced.