Mathematics
Grade9
Easy

Question

In the given figure, if the exterior angle is 135o, then ∠P is

  1. 45°
  2. 60°
  3. 80°
  4. 90°

The correct answer is: 90°


    G i v e n comma
E x t e r i o r space angle R space equals space 135 degree
Q P space equals space P R

T o space f i n d comma
angle P

H e r e comma
Q P space equals space P R
therefore space angle R space equals space angle Q space open parentheses t h e space a n g l e s space o p p o s i t e space t o space t h e space c o n g r u e n t space s i d e s space a r e space a l s o space e q u a l close parentheses

W e space k n o w space t h a t comma
angle R space plus space e x t e r i o r space angle R space equals space 180 degree
angle R space plus space 135 degree space equals space 180 degree
angle R space equals space 180 degree space minus space 135 degree space equals space 45 degree

therefore angle Q space equals space angle R space equals space 45 degree

T h e space s u m space o f space a l l space a n g l e s space o f space a space t r i a n g l e space i s space 180 degree
angle P space plus space angle Q space plus space angle R space equals space 180 degree
angle P space plus space 45 degree space plus space 45 degree space equals space 180 degree
angle P space plus space 90 degree space equals space 180 degree
angle P space equals space 180 degree space minus space 90 degree space equals space 90 degree

therefore space angle P space equals space 90 degree

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