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Adjacent angles
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Adjacent angles If two angles have the same vertex and a common ray, then the angles are called adjacent angles. In Fig, ∠BAC and ∠CAD are adjacent angles (i.e ∠ x and ∠y) as they have common ray.
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Adjacent angles on a line
When a ray stands on a straight line two angles are formed. They are called linear adjacent angles on the line. In Fig, ∠AOC and ∠BOC are adjacent angles on a line as they have common ray.
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The sum of the adjacent angles on a line is 180°
∠ AOB=1800 is a straight angle. In fig. The ray OC stands on a line AB. ∠AOC and ∠COB are adjacent angles. ∠AOB is a straight angle whose measure is 180° So, ∠AOC + ∠COB = 180° Thus the sum of the adjacent angles on a line is 180° Note 1: A pair of adjacent angles whose non common rays are opposite rays. Note 2: Two adjacent supplementary angles form a straight angle.
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Adjacent angles example
Example 1: From the figure, Identify a) Two pairs of adjacent angles. Solution: Two pairs of Adjacent angles. ∠EOC and ∠BOE (As shown in the fig, ∠1 and ∠2 are adjacent) (since OE is common to ∠EOC and ∠ BOE) ∠BOC and ∠BOD (As shown in the fig, ∠3 and ∠4 are adjacent) (since OB is common to ∠BOC and ∠BOD)
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Example 2: Find the value of x in the given figure.
Solution: Given: From the figure , ∠BCD = 45° and ∠DCA = x ∠BCD and ∠DCA are adjacent angles on a straight line. We know that sum of the adjacent angles on a straight line is 180° ∠BCD + ∠DCA = 180° 45° x = 180° x = 180° - 45° x = 135° Therefore, the value of x is 135° Since ∠BCA = 180° is a straight angle
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Example 3: Find the value of x in the given figure.
Solution: Given: From the figure , ∠BCD = 40° , ∠DCE = x and ∠ECA = 30° ∠BCD , ∠DCE and ∠ECA are adjacent angles on a straight line. We know that sum of the adjacent angles on a straight line is 180° ∠BCD + ∠DCA + ∠ECA = 180° 40° + x ° = 180° 70° x = ° x = ° - 70° x = ° Therefore, the value of x is 110° Since ∠BCA = 180° is a straight angle
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Try these 1. Find the value of x in the given figure
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