Question

pls help me out please and those don't answer who don't know the answer​

Answer 1

Answer:

2. (a) You know angle sum of property of a quadrilateral

i.e., Sum of all angles of a quadrilateral = 360°

Now, x + 140 + 80 + 40 = 360

x + 260 = 360

Hence, ∠x = 100°

(b) Again sum of all angles of the quadrilateral = 360°

So, x + 100 + 105 + 55 = 360

x + 260 = 360

Hence, ∠ x = 100°

3. Remember formula for finding diagonals in a polygon of 'n' sides, i.e.,

number of diagonals = $\frac{n(n-3)}{2}$

(a) 3 sided polygon, so, n = 3.

Number of diagonals = $\frac{3(3-3)}{2}$ = 0 diagonals

(b) 5 sided polygon, so, n = 5

Number of diagonals = $\frac{5 (5-3)}{2}$ = 5 diagonals

(c) 7 sides polygon, so, n = 7

Number of diagonals = $\frac{7(7-3)}{2}$ = 14 diagonals

4. (a) Here First we find the all interior angles of the triangle by linear pair axiom,

firstly, 130 + a = 180 ⇒ a = 50°

and, 105 + b = 180 ⇒ b = 75°

simultaneously, x + c = (180 - x)°

Now using angle sum property of triangle,

a + b + c = 180

50 + 75 + 180 - x = 180

x = 125°

(b) Again we find all interior angles of the quadrilateral by linear pair axiom as in part (a), that come out to be,

a = 70, b = 140, c = 90, d = 180 - x, e = 120

Now, using angle sum property of a quadrilateral as in q. 2.,

a + b + c + d + e = 360°

70 + 140 + 90 + 180 - x + 120 = 360

x = 240°

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