taytayswizzle27
Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

A triangle with an angle measure of 40° was cut into 6 triangles by its angle bisectors. Some of these new triangles are right triangles. What could be the measure of the largest angle of this triangle?

Sagot :

livracette

Answer: :)

Step-by-step explanation:

By the Angle Bisector Theorem,

BDDC=ABAC

Proof:

Draw BE←→∥AD←→

.

Extend CA⎯⎯⎯⎯⎯

to meet BE←→ at point E

.

By the Side-Splitter Theorem,

CDDB=CAAE

---------( 1

)

The angles ∠4and∠1

are corresponding angles.

So, ∠4≅∠1

.

Since AD⎯⎯⎯⎯⎯

is a angle bisector of the angle ∠CAB,∠1≅∠2

.

By the Alternate Interior Angle Theorem , ∠2≅∠3

.

Therefore, by transitive property, ∠4≅∠3

.

Since the angles ∠3and∠4

are congruent , the triangle ΔABE is an isosceles triangle with AE=AB

.

Replacing AE

by AB in equation ( 1

),

CDDB=CAAB

Example:

Find the value of x

.

By Triangle-Angle-Bisector Theorem,

ABBC=ADDC

.

Substitute.

512=3.5x

Cross multiply.

5x=42

Divide both sides by 5

.

5x5=425x=8.4

The value of x

is 8.4 .

The largest angle is 8.4.

what is Angle-Bisector theorem?

The Angle-Bisector theorem in geometry is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into. It compares their proportional lengths to the proportional lengths of the triangle's other two sides.

Given

By the Angle Bisector Theorem,

BDDC=ABAC

Proof:

Draw BE←→∥AD←→

Extend CA��⎯⎯⎯⎯to meet BE←→ at point E

By the Side-Splitter Theorem,

CDDB=CAAE---------( 1)

The angles ∠4and∠1

are corresponding angles.

So, ∠4≅∠1

Since AD⎯⎯⎯⎯⎯

is a angle bisector of the angle ∠CAB,∠1≅∠2

By the Alternate Interior Angle Theorem , ∠2≅∠3

Therefore, by transitive property, ∠4≅∠3

Since the angles ∠3and∠4

are congruent , the triangle ΔABE is an isosceles triangle with AE=AB

Replacing AE

by AB in equation ( 1),

CDDB=CAAB

Example:

Find the value of x

By Triangle-Angle-Bisector Theorem,

ABBC=ADDC

Substitute.

512=3.5x

Cross multiply.

5x=42

Divide both sides by 5

5x/5=42/5=8.4

The value of x is 8.4 .

To learn more about the angle-bisector theorem refer to:

https://brainly.com/question/2478436

#SPJ2

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.