Question

4. Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the figure. Find the measure of the acute angle formed by the intersection of Walnut Street and Elm Street.

Answer 1

Answer:

Step-by-step explanation:

since elm parallel to oak , by alternate interior angle-

2x+33 =5x-15

x=16

thus 2x+33 =65

Answer 2

$\huge\bold{{\pink{Q}}{\blue{U}}{\green{E}}{\red{S}}{\purple{T}}{\orange{I}}{\pink{O}}{\blue{N}}{\green{❥}}}$

Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the figure. Find the measure of the acute angle formed by the intersection of Walnut Street and Elm Street.

$\huge\bold{{\pink{G}}{\blue{I}}{\green{V}}{\red{E}}{\purple{N}}{\green{❥}}}$

• Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street.

$\huge\bold{{\pink{T}}{\blue{O}}{\green{  }}{\red{F}}{\purple{I}}{\orange{N}}{\pink{D}}{\green{❥}}}$

• The measure of the acute angle formed by the intersection of Walnut Street and Elm Street.

$\huge\bold{{\pink{S}}{\blue{O}}{\green{L}}{\red{U}}{\purple{T}}{\orange{I}}{\pink{O}}{\blue{N}}{\green{❥}}}$

In the attached image,

• $\blue{\boxed{\pink{CD|| EF}}}$

• $\pink{\boxed{\blue{AB\:is\:the\: transversal.}}}$

• $\green{\boxed{\orange{AB\:cuts\:CD\:at\:O.}}}$

• $\purple{\boxed{\red{AB\:cuts\:EF\:at\:P.}}}$

So, ∠AOP and ∠EPO are opposite interior angles.

We know that if two lines are parallel, the opposite interior angles, formed by the intersection of the lines by a transversal, are equal.

So,

$(2x+33)=(5x-15)$

$➳\:2x-5x=(-15)-33$

$➳\:-3x=-48$

$➳\:x={\frac{-48}{-3}}$

$➳\:x=16$

$\huge\bold{{\pink{H}}{\blue{E}}{\green{N}}{\red{C}}{\purple{E}}{\green{❥}}}$

$x=16$

$2x+33=(2×16)+33=32+33=65$

$5x-15=(5×16)-15=80-15=65$

$\huge\bold{{\pink{T}}{\blue{H}}{\green{E}}{\red{R}}{\purple{E}}{\orange{F}}{\pink{O}}{\blue{R}}{\red{E}}{\green{❥}}}$

The measure of the acute angle formed by the intersection of Walnut Street and Elm Street is 65°.

$\huge\bold{{\pink{D}}{\blue{O}}{\green{N}}{\red{E}}{\purple{࿐}}}$

$\bold\green{\boxed{{\blue{✿}}{\pink{H}}{\blue{O}}{\green{P}}{\red{E}}{\purple{  }}{\orange{T}}{\pink{H}}{\blue{I}}{\green{S}}{\red{  }}{\purple{H}}{\orange{E}}{\pink{L}}{\blue{P}}{\green{S}}{\red{  }}{\purple{Y}}{\orange{O}}{\pink{U}}{\blue{✿}}}}$

$\bold\red{\boxed{{\blue{✿}}{\pink{H}}{\blue{A}}{\green{V}}{\red{E}}{\purple{  }}{\orange{A}}{\pink{  }}{\blue{N}}{\green{I}}{\red{C}}{\purple{E}}{\purple{  }}{\orange{D}}{\pink{A}}{\green{Y}}{\blue{✿}}}}$