Question

60. The measures of two alternate angles formed by a transversal
to two parallel lines are 2x + 10 and 3x - 20. Then, the
measure of each angle is​

Answer 1

Step-by-step explanation:

We are given two parallel lines

AB

↔

and

CD

by azeeza.r

↔

, and transversal

PQ

↔

. Consider the pair of alternate angles ∠ALM and ∠LMD.

Let

LX

→

be the bisector of ∠ALM and

MY

→

be the bisector of ∠LMD.

Extend the ray

LX

→

to the straight line

XR

↔

and the ray

MY

→

to the straight line

SY

→

as shown in the figure(see Fig).

We have to show that

XR

↔

∥

SY

↔

. Consider the lines

XR

↔

and

SY

↔

with transversal

PQ

↔

.

We have,

∠XLM=

2

1

∠ALM and ∠LMY=

2

1

∠LMD.

However, ∠ALM=∠LMD ........ (Alternate angles made by same transversal PQ)

We hence obtain ∠XLM=∠LMY.

But ∠XLM and ∠LMY are a pair of alternate angles made by the transversal

PQ

↔

with the lines

XR

↔

and

SY

↔

.

Hence, we conclude that

XR

↔

∥

SY

↔