Name: Measure of an Angle
Uploaded: 2019-07-19
Duration: 1 min 48 s
Description: An angle made by two line segments is measured using a geometrical tool called the protractor. A complete angle around a point is 360 degrees. Watch this vid...

Question

In the adjoining diagram, $D E ∥ B C$ . Find the value of $x$ .

Accepted Answer

In the triangle $C D E$ ,

$∠ C D E + ∠ D C E + ∠ C E D = 180 °$ (Angles inside a triangle)

$27 ° + 23 ° + ∠ C E D = 180 °$

$50 ° + ∠ C E D = 180 °$

$∠ C E D = 180 ° - 50 °$

$∠ C E D = 130 °$

In the adjoining diagram, $D E ∥ B C$ , so $C D$ acts as the transversal.

$∠ C E D + ∠ B C E = 180 °$ (Pair of interior angles on the same side of transversal)

$∠ C E D + ∠ B C D + ∠ D C E = 180 °$

$130 ° + ∠ B C D + 23 ° = 180 °$

$∠ B C D + 153 ° = 180 °$

$∠ B C D = 180 ° - 153 °$

$∠ B C D = 27 °$

In the triangle $∆ A B C$ ,

$∠ B A C + ∠ A B C + ∠ B C A = 180 °$

$∠ B A C + ∠ A B C + ∠ B C D + ∠ D C A = 180 °$

$x + 62 ° + 27 ° + 23 ° = 180 °$

$x + 112 ° = 180 °$

$x = 180 ° - 112 °$

$x = 68 °$

Hence, the value of $x$ is $68 °$ .

M L Aggarwal Solutions for Chapter: Lines and Angles, Exercise 5: Higher Order Thinking Skills (HOTS)

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Lines and Angles, Exercise 5: Higher Order Thinking Skills (HOTS)

Questions from M L Aggarwal Solutions for Chapter: Lines and Angles, Exercise 5: Higher Order Thinking Skills (HOTS) with Hints & Solutions

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