Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 29

In the figure above, \(\overline{F G} \| \overline{J K}, F G=J K\), and \(G H=H J\). What is the measure of angle \(J\) if \(F K=H J(\sqrt{2})\) ? A) \(90^{\circ}\) B) \(120^{\circ}\) C) \(135^{\circ}\) D) \(160^{\circ}\)

Short Answer

Expert verified
A) \(90^{\circ}\)

Step by step solution

01

Identify angle relationships

Since FG is parallel to JK, we can see that angles FGH and JHJ are alternate interior angles and thus equal. Angle H is then the exterior angle of triangle JHK.
02

Find angle HFK

Use the fact that the sum of the interior angles of a triangle equals 180 degrees. The triangles GHF and FHK are right-angled triangles as their sides are proportional to the sides of a 45-45-90 degree triangle. So, we have angle F = angle H = 45 degrees. Now, angle HFK = angle F + angle H = 45 + 45 = 90 degrees.
03

Apply the Exterior Angle Theorem

Since angle H is the exterior angle of triangle JHK and angle HFK is 90 degrees (right angle), by the Exterior Angle Theorem, we can find angle J. The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. \[ \angle J = \angle JHK + \angle F \]
04

Calculate angle J

We know that angle F and angle JHK are both 45 degrees. Now, substitute these values: \[ \angle J = 45 + 45 = 90 \] The measure of angle J is 90 degrees. Therefore, the correct answer is: A) \(90^{\circ}\).

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.

Start your free trial

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

Most popular questions from this chapter

Samantha offers two different packages of yoga classes at her yoga studio. She offers two hot yoga sessions and three zero gravity yoga sessions at a total cost of $$\$ 400$$. She also offers four hot yoga sessions and two zero gravity sessions at a price of $$\$ 440$$. Samantha wants to offer a larger package for long-time clients in which the cost must exceed \(\$ 800\). If Samantha does not wish to include more than

If \(x^2+2 x y+y^2=64\) and \(y-x=12\), which of the following could be the value of \(x\) ? A) \(-10\) B) \(-4\) C) 2 D) 10

The author indicates that prior to the Stanford University study the scientists generally believed that antibiotic-resistant strains of tuberculosis A) had a better chance of survival than their antibiotic-susceptible ancestors. B) would once again become the most deadly of diseases. C) resulted in lowered amounts of sputum in those they infect. D) did not have a survival rate equal to that of non-resistant strains.

A) NO CHANGE B) they're C) its D) it's

$$ 8 a+20=7+\frac{3}{4}(8 a+20) $$ Based on the equation above, which of the following is equal to \(2 a+5\) ? A) \(-7\) B) \(-\frac{5}{2}\) C) 7 D) 10
See all solutions

Recommended explanations on English Textbooks

Prosody

Read Explanation

Essay Prompts

Read Explanation

Pragmatics

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Phonetics

Read Explanation

Rhetoric

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free