verify the given sum
Answers
Answer:
1. (x+y)+z=x+(y+z) verified
2. 120∘, 60∘, 120∘, 60∘
Step-by-step explanation:
1.
x=½, y=⅔, z=-1/5
(x+y)+z =x+(y+z)
(1/2+2/3)+(-1/5)=1/2+[2/3+(-1/5)]
[(3×1+2×2)/2×3]-1/5=1/2+[(2×5-1×3)/3×5]
[(3+4)/6]-1/5=1/2+[(10-3)/15]
7/6-1/5=1/2+7/15
(7×5-6×1)/6×5=(1×15+7×2)2×15
(35-6)/30=(15+14)/30
29/30=29/30
2.
ABCD is a rhombus.
⇒AC=BC ........(1)(given)
BC=AB .....(2)(side of rhombus)
From eqns(1) and (2)
AC=BC=AB
⇒△ABC is equilateral triangle.
So, ∠ABC=60
∘
∠BCA=60
∘
..........(3)
∠CAB=60
∘
..........(4)
Similarly, in △ADC,AD=DC(sides of a rhombus)
AD=BC
But BC=AC
∴AD=AC
∴AD=DC=AC
∴DAC is an equilateral triangle.
⇒∠CAD=60
∘
......(5)
⇒∠ADC=60
∘
⇒∠DCA=60
∘
.......(6)
From eqns(3) and (6) we get
∠BCA+∠DCA=60
∘
+60
∘
=120
∘
∴∠C=120
∘
From eqns(4) and (5),
∠CAB+∠CAD=60
∘
+60
∘
=120
∘
∴∠A=120
∘
Hence the four angles of the Rhombus are
120∘, 60∘, 120∘, 60∘