Mathematics
Grade9
Easy

Question

In the given figure, PS is the median, bisecting angle P, then angleQPS is

  1. 110°
  2. 70°
  3. 45°
  4. 55°

hintHint:

S o l v e space f o r space angle P space b y space a p p l y i n g space t h e space apostrophe 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 apostrophe.

The correct answer is: 45°


    G i v e n comma
angle Q space equals space 45 degree
P S space i s space t h e space m e d i a n

T o space f i n d comma
angle Q P S

H e r e comma
P S space i s space t h e space m e d i a n. space
therefore space angle P S Q space equals space 90 degree

W e space k n o w space t h a t space t h e space s u m space o f space a l l space t h e 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
H e n c e comma space f o r space increment Q P S
angle Q space plus space angle P space plus space angle S space equals space 180 degree
45 degree space plus space angle P space plus space 90 degree space equals space 180 degree
angle P space plus space 135 degree space equals space 180 degree
angle P space equals space 180 degree space minus space 135 degree
angle P space equals space space 45 degree

T h e r e f o r e comma space space angle Q P S space equals space space 45 degree

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