Question

if all the lines on the given figure a straight line then what is the value of A + B + C + D + E + F?​

Answer 1

Answer:

45+45+45+45+45+45 = 270

Step-by-step explanation:

If all are the straight line then there is 90 degree one angle and tje remaining angles are equal because all are the straight line and the two equal sides of an isosceles triangle are 45 degree

Answer 2

Given:

All the lines are straight

To find:

The value of angle a+angle b+angle c+angle d+angle e+angle f

Solution:

The required value of angle a+angle b+angle c+angle d+angle e+angle f is 360°.

We will use the property of getting the angles' sum of any triangle equal to 180° to determine the required value.

Let us name all the given triangles as in the figure.

Now, in ΔABC, angle a+angle b+angle ACB=180°

Angle ACB=180°-angle a-angle b (1)

Similarly, in ΔDEF, angle e+angle f+angle EDF=180°

Angle EDF=180°-angle e-angle f (2)

In ΔGHI, angle c+angle d+angle HGI=180°

Angle HGI=180°-angle c-angle d (3)

We are given that all the lines are straight.

So, angle ACB=angle GCD

angle EDF=angle GDC

angle HGI=angle DGC (All these angles are vertically opposite to each other)

Now, using the similar property, in ΔGDC

angle GCD+angle GDC+angle DGC=180°

From (1), (2), and (3),

(180°-angle a-angle b)+(180°-angle e-angle f)+(180°-angle c-angle d)=180°

180°-angle a-angle b+180°-angle e-angle f+180°-angle c-angle d=180°

180×3-180= angle a+angle b+angle c+angle d+angle e+angle f

360°=angle a+angle b+angle c+angle d+angle e+angle f

Therefore, the required value of angle a+angle b+angle c+angle d+angle e+angle f is 360°.