B E 13. In each of the following figures, one side of a triangle has been produced. Find all the angles of the triangle in each case.
[tex]exterior \: angle \: = \: sum \: of \: interior \: opposite \: angle[/tex]
[tex]exterior \: angle \: = \: sum \: of \: interior \: opposite \: angle[/tex]
Answers & Comments
Question - iv)
➟ ∠ABC = 180° - ∠EBC⠀⠀(∠s on a straight line)
➟ y° = 180° - 140°
➟ y° = 40°
➟ ∠ACB = 180° - ∠ACD⠀⠀(∠s on a straight line)
➟ z° = 180° - 130°
➟ z° = 50°
➟ x° + y° + z° = 180°⠀⠀(Sum of ∠s of a ∆)
➟ x° + 40° + 50° = 180°
➟ x° + 90° = 180°
➟ x° = 180° - 90°
➟ x° = 90°
Question - vi)
➟ ∠ABC = 180° - ∠DBC⠀⠀(∠s on a straight line)
➟ ∠ABC = 180° - 130°
➟ ∠ABC = 50°
➟ ∠ABC + ∠BAC + ∠ACB = 180°⠀⠀(Sum of ∠s of a ∆)
➟ 50° + x° + x° = 180°
➟ 2x° = 180° - 50°
➟ 2x° = 130°
➟ x° = 130/2
➟ x° = 65°
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