Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

For exercises 3 and 4 you are given that OBland OAOC.

If m3=t, express the measures of the other numbered angles in terms of t.

Short Answer

Expert verified

The values of the measure of the angles ∠4, ∠5 and ∠6 are 90°t, and90°t respectively.

Step by step solution

01

Step 1. Label the given diagram.

Label the given diagram as:

02

Step 2. Find the measure of the angle ∠4.

AsOBl,therefore the lines OB and I are perpendiculars.

Therefore, by using the definition of perpendicular lines, the measure of the angleBOE is 90°.

That implies, mBOE=90°.

By using the angle addition postulate:

mBOE=m4+m3

By using the relation mBOE=90°, it can be obtained that:

90°=m4+m31

Substitute t form3 into the equation (1).

90°=m4+m390°=m4+t90°t=m4

Therefore, the measure of the angle ∠4 is 90°t.

03

Step 3. Find the measure of the angle ∠5.

As OAOC,therefore the lines OA and OC are perpendicular.

Therefore, by using the definition of perpendicular lines, the measure of the angle∠AOC is 90° .

That implies, mAOC=90°.

By using the angle addition postulate:

mAOC=m5+m4

By using the relation mAOC=90°, it can be obtained that:

90°=m5+m42

Substitute 90°tfor m4into the equation (2).

90°=m5+m490°=m5+90°t90°90°+t=m5t=m5

Therefore, the measure of angle ∠5 is t.

04

Step 4. Find the measure of the angle ∠6.

As OBl,therefore the lines OB and I are perpendiculars.

Therefore, by using the definition of perpendicular lines, the measure of the angle BOD is 90°.

That implies, mBOD=90°.

By using the angle addition postulate:

mBOD=m5+m6

By using the relation mBOD=90°, it can be obtained that:

90°=m5+m63

Substitute t for m∠5into the equation (3).

90°=m5+m690°=t+m690°t=m6

Therefore, the measure of angle ∠6 is 90°t.

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 Vaia!

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.

Sign-up for free