Asksia AI LOGO

Sia

Question
Math
Posted 2 months ago

In the figure below, APE\angle A P E and EPD\angle E P D are congruent.
What is the arc measure of major arc BAundefinedDB \widehat{A} D on circle PP in degrees?
Sign in to unlock the answer
Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
To find the measure of major arc BAundefinedDB \widehat{A} D, we first need to determine the measure of the central angle APD\angle APD that intercepts it
step 2
Since APE\angle APE and EPD\angle EPD are congruent, we can express APD\angle APD as the sum of APE\angle APE and EPD\angle EPD
step 3
The sum of all central angles in a circle is 360360^\circ. We can calculate the measure of APE\angle APE (and EPD\angle EPD) by subtracting the measures of APB\angle APB, BPC\angle BPC, and CPD\angle CPD from 360360^\circ and then dividing by 2, because there are two congruent angles
step 4
Subtracting the given angles from 360360^\circ: 3601367442=108360^\circ - 136^\circ - 74^\circ - 42^\circ = 108^\circ
step 5
Dividing 108108^\circ by 2 to find the measure of APE\angle APE and EPD\angle EPD: 108/2=54108^\circ / 2 = 54^\circ
step 6
Now, we can find the measure of APD\angle APD by adding the measures of APE\angle APE and EPD\angle EPD: 54+54=10854^\circ + 54^\circ = 108^\circ
step 7
The measure of major arc BAundefinedDB \widehat{A} D is the difference between 360360^\circ and the measure of APD\angle APD: 360108=252360^\circ - 108^\circ = 252^\circ
Answer
The arc measure of major arc BAundefinedDB \widehat{A} D on circle PP is 252252^\circ.
Key Concept
Central and Inscribed Angles
Explanation
The measure of a major arc is found by subtracting the central angle that intercepts the minor arc from 360360^\circ. In this case, the major arc is opposite the central angle APD\angle APD.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question