Question

in the given figure prove that angle p + angle q + angle r + angle s + angle t = 2 right angles​

Answer 1

TO FIND :

angle p + angle q + angle r + angle s + angle t = 2 right angles​

SOLUTION :

◆ABCDE is a pentagon , since interior angles of a pentagon is 108°

◆Ang 1 = 108 ° , And similarly all angles 1,2,3,4,5 =108°

◆Angles P,Q,R,S,T are equal , since In a symmetric figure, all triangles attached to sides of a Pentagon is congruent.

◆Consider, Line segment PR,

< 1 = 108°,

<BAR = 180 - 108 =72° ,

(Since Total angle in a line is 180°)

◆Similarly, <ABR = 72° ,

◆We know,

Total angle in a triangle = 180°

<BAR + <ABR + < R = 180°

Substituting values,

72° + 72°+ <R = 180°

< R = 36°

◆Since <P= <.Q=< R=< S=< T,

◆<P+ <.Q+< R+< S+< T=72° × 5 =180°.

Hence the solution.

Answer 2

Answer:

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