Question

Find the sum of a + b + c + d in the following figures.
(a)
105°
950
609
110° /​

Answer 1

Answer:

For 1st figure,

A=120

B=60(similar to D above)

C=75

D=105

Now,120+60+75+105

=360

This is for 2nd figure..

A=180-70=110

B=180-95=85

C=180-110=70

D=180-{360-(110+70+95)}

=180-85

=95

Now,110+85+70+95

=350

Step-by-step explanation:

Note:sum of all angles of quadrilateral is 360°And, sum of angles on a line is 180°

Answer 2

Answer:

a) angle a + 60° = 180°( Angle in a straight line)

angle a= 180°-60°=120°

angle b= 60° (Alternating angle)

angle d+75°=180°(Angle in a straight line)

angle d=180°-75°=105°

angle c+105°=180°(Angle in a straight line)

angle c=180°-105°=75°

Now,

a+b+c+d=120+60+75+105=180+180=360°

b)angle a+ 70°=180°(Angle in a straight line)

angle a=180°-70°=110°

angle c+110°=180°(Angle in a straight line)

angle c=180°-110°=70°

angle b +95°=180°(Angle in a straight line)

angle b=180°-95°=85°

If we see the quadrilateral,

70°+110°+95°+x°=360°

275°+x°=360°

x°=360°-275°=85°

angle d +85°=180°(Angle in a straight line)

angle d=180°-85°=95°

Now,

a+b+c+d=110°+85°+70°+95°=360°