## Plane Geometry

#### Plane Geometry

1. If angles of measure (5y + 62°) and (22° + y) are supplementary, then value of y is :

1. As we know that Sum of two supplementary angles = 180°
∴ ( 5y + 62° ) + ( 22° + y ) = 180°
⇒ 6y + 84° = 180°
⇒ 6y = 180° – 84° = 96°

##### Correct Option: A

As we know that Sum of two supplementary angles = 180°
∴ ( 5y + 62° ) + ( 22° + y ) = 180°
⇒ 6y + 84° = 180°
⇒ 6y = 180° – 84° = 96°

 ∴ y = 96 = 16° 6

1. In, ΔABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

1. Clearly DE || BC (by converse of BPT)

##### Correct Option: B

Clearly DE || BC (by converse of BPT) ∴ ΔADE ∼ ABC (∠A = ∠A and ∠ADE = ∠B)

1. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.

1. Draw a figure as per given question,
In ΔACB and PCQ
∠C = ∠C (common)
∠ABC = ∠PQC (each 90°)
∴ ΔACB ∼ ΔPC (AA Similarity)

##### Correct Option: C

In ΔACB and PCQ
∠C = ∠C (common)
∠ABC = ∠PQC (each 90°)
∴ ΔACB ∼ ΔPC (AA Similarity)

 ∴ AB = BC PQ QC

 h = 4000 12 8

h = 60m

1. In the given figure, find the length of BD.

1. In Δs ADE and ΔABC
∠A = ∠A [common]
∠ADE = ∠ACB = x° (Given)
∴ ΔADE ∼ ΔACB ( AA Similarly)

##### Correct Option: A

∠A = ∠A [common]
∴ ΔADE ∼ ΔACB (AA Similarly)

 AD = AE (corresponding side of ⁓ ∆s are proportional) AC AB

 6 = 9 13 AB

 AB = 39 = 19.5 cm 2

Hence BD = AB - AD = 19.5 - 6 = 13.5 cm.

1. ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then ∠BCD is :

1. As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

Given , ∠COD = 120°
∠BAC = 30°

 ∠CAD = 1 × ∠COD 2

 ∠CAD = 1 × 120° = 60° 2

##### Correct Option: B

As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

Given , ∠COD = 120°
∠BAC = 30°

 ∠CAD = 1 × ∠COD 2

 ∠CAD = 1 × 120° = 60° 2