Mathematics

Problem

The side rails

\text{R}_1

and

\text{R}_2

of a pedestrian bridge are meant to be parallel. To check this, an engineer fits two diagonal braces

\text{S}

and

\text{T}

that intersect both rails. • Brace

\text{S}

makes an angle of

(4y - 10)^\circ

with

\text{R}_1

and an alternate interior angle of

(2y + 50)^\circ

with

\text{R}_2

. • Brace

\text{T}

makes co-interior angles of

120^\circ

with

\text{R}_1

and

60^\circ

with

\text{R}_2

on the same side. Which of the following statements is correct? a)

\text{R}_1

and

\text{R}_2

are parallel and

y = 15

. b)

\text{R}_1

and

\text{R}_2

are parallel and

y = 30

. c)

\text{R}_1

and

\text{R}_2

are parallel and

y \;\approx\; 23.3

. d)

\text{R}_1

and

\text{R}_2

are not parallel because the co-interior angles with brace

\text{T}

are not equal.