Question

Page No.: In the figuze given below, line | || line m. find angle a, Angle b, angle c, angle d and angle c and angle f. using the measures given​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let us,

Name the points as shown in figure.

Given :

$line \: \ell \: \parallel \: line \: m\\ \angle JWT = 136 \degree \\ \angle XZY = 85 \degree \:$

To find :

$\angle a \: , \angle \: b \: , \angle c \: , \angle d \: , \angle e \: , \angle f$

Solution :

$\displaystyle \: line \: \ell \: \parallel \: line \: m \\ \: and \: line \: p \: is \: their \: transversal$

$1) \: \angle a \\ \angle \: JWT = \angle \: XWK \\ - ( Vertically \: opposite \: angles ) \\ \boxed {\angle \: a = 136 \degree}$

$2) \: \angle b \\ \angle \: JWT = \angle \: GXW \: \\ - ( Corresponding \: angles ) \\ \boxed {\angle \: b \: = 136 \degree}$

$3) \: \angle c \\ \angle b + \angle c = 180 \degree \\ - ( Angles \: in \: linear \: pair ) \\ 136 \degree + \angle \: c \: = 180 \degree \: \\ \angle \: c = 180 \degree - 136 \degree \: \\ \boxed { \angle \: c = 44 \degree}$

Now taking,

$line \: \ell \parallel \: line \: m \: \\ and \: q \: is \: their \: transversal$

$4) \: \angle d \\ \angle \: XZY = \angle WYU \\ - ( Corresponding \: angles ) \\ \boxed {\angle \: d = 85 \degree}$

$5) \: \angle e \\ \angle \: d = \angle \: e \\ - ( Vertically \: opposite \: angles ) \\ \boxed {\angle \: e = 85 \degree}$

$6) \angle f \\ \angle \: d + \angle f = 180 \degree \\ - ( Angles \: in \: linear \: pair ) \\ 85 \degree + \angle \: f = 180 \degree \\ \angle \: f = 180 \degree - 85 \degree \\ \boxed{\angle \: f = 95 \degree}$

[ Note : Refer the figure ]