In a cyclic quadrilateral two adjacent angles are 40 ° and π c 3 . Find the angles of the quadrilateral in degree.

Let A B C D be the given cyclic quadrilateral. ∠ A = 40 ° and ∠ B = π 3 c Now, the measures in radian can be converted to into degree using π c = 180 ∘ . Therefore, ∠ B = π C 3 = 180 3 ∘ = 60 ∘ . We know that, sum of opposite angles in a cyclic quadrilateral are supplementary Therefore, ∠ A + ∠ C = 180 ° , ∠ B + ∠ D = 180 ° Consider ∠ A + ∠ C = 180 ° ⇒ 40 ° + ∠ C = 180 ° ⇒ ∠ C = 180 ° - 40 ° ⇒ ∠ C = 140 ° Now, ∠ B + ∠ D = 180 ° ⇒ 60 ° + ∠ D = 180 ° ⇒ ∠ D = 180 ° - 60 ° ⇒ ∠ D = 120 ° Hence ∠ A = 40 ° , ∠ B = 60 ° , ∠ C = 140 ° , ∠ D = 120 °

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Mathematics and Statistics (Arts & Science) Part 1>Chapter 1 - Angle and its Measurement>EXERCISE 1.1

Maharashtra Board Solutions for Chapter: Angle and its Measurement, Exercise 1: EXERCISE 1.1

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Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Angle and its Measurement, Exercise 1: EXERCISE 1.1

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Questions from Maharashtra Board Solutions for Chapter: Angle and its Measurement, Exercise 1: EXERCISE 1.1 with Hints & Solutions

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 1 - Angle and its Measurement>EXERCISE 1.1>Q 9

The measures of the angles of a triangle are in the ratio $3 : 7 : 8$ . Find their measures in degree and radian.

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 1 - Angle and its Measurement>EXERCISE 1.1>Q 10

The measures of the angles of a triangle are in $A . P .$ and the greatest is $5$ times the smallest (least). Find the angles in degree and radian.

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 1 - Angle and its Measurement>EXERCISE 1.1>Q 11

In a cyclic quadrilateral two adjacent angles are $40 °$ and $\frac{π^{c}}{3} .$ Find the angles of the quadrilateral in degree.

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 1 - Angle and its Measurement>EXERCISE 1.1>Q 12

One angle of a quadrilateral has measure $\frac{2 π^{c}}{5}$ and the measures of other three angles are in the ratio $2 : 3 : 4 .$ Find their measures in degree and radian.