/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q5. In the diagram, BE→⊥AC↔ a... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

In the diagram, BE→⊥AC↔and BD→⊥BF→. Find the measures of the following angles.

m∠CBF

m∠EBF

m∠DBE

m∠DBA

m∠DBC

x

?

?

?

?

Short Answer

Expert verified

The following table represents the required solution:

m∠CBF

m∠EBF

m∠DBE

m∠DBA

m∠DBC

x

90-x

x

90-x

90+x

Step by step solution

01

Step 1. Observe the given information.

As the measurement of angle CBF is already given and the perpendicular relationship between the given lines represents that the measurement of ∠ABE,∠CBE and∠DBF is equal to 90°.

02

Step 2. Determine the value of m∠EBF, m∠DBE, m∠DBA and m∠DBC. 

According to the figure ∠EBFand ∠CBFmakes the right ∠EBCso by using this determines the value of ∠EBF.

∠EBC=∠EBF+∠CBF90=∠EBF+x∠EBF=90-x

According to the figure∠EBF and∠DBE makes the right∠DBFso by using this determines the value of ∠DBE.

∠DBF=∠EBF+∠DBE90=90-x+∠DBE∠DBE=90-90+x∠DBE=x

According to the figure∠DBA and∠DBE makes the right∠ABEso by using this determines the value of ∠DBA.

∠ABE=∠DBA+∠DBE90=∠DBA+x∠DBA=90-x

According to the figure the right∠DBF and∠CBF makes∠DBCso by using this determines the value of ∠DBC.

∠DBC=∠DBF+∠CBF=90+x

03

Step 3. Make the complete table.

Make the complete table by writing the value of obtained angles into their respective columns.

m∠CBF

m∠EBF

m∠DBE

m∠DBA

m∠DBC

x

90-x

x

90-x

90+x

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.