Question

find the value of a,b,c
by step by step ​

Answer 1

Answer:

Step-by-step explanation:

80+40+b=180

b=180-120

b=60

B=a =80(alternate interior angle)

C=c=40(alternate interior angle)

to verify, 60+80+40=180

Hope , it helpful for u

Answer 2

Answer:

Step-by-step explanation:

Given:

$\texttt{P is parallel to BC.}$

$\mathtt{\angle B = 80^\circ}$

$\mathtt{\angle C = 40^\circ}$

To find:

$\mathtt{1. \:\:\angle a}$

As, line P is parallel to line BC and AB is a transversal.

Then,

$\mathtt{\angle A = \angle B = 80^\circ}$                                                             [alternate interior angles.]

$\mathtt{2. \:\:\angle b}$

As, ABC is a triangle.

Then,

$\mathtt{\angle B + \angle C + \angle b = 180^\circ}$                               [sum of all angles of a triangle is 180.]

$\implies \mathtt{80^\circ+40^\circ+\angle b=180^\circ}$

$\implies \mathtt{\angle b=180^\circ-80^\circ-40^\circ}$

$\implies \mathtt{\angle b= 60^\circ}$

$\mathtt{3. \:\:\angle c}$

As, line P is parallel to line BC and AC is a transversal.

Then,

$\mathtt{\angle c = \angle C= 40^\circ}$                                                             [alternate interior angles.]