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Transcript

Chords, Arcs and Central Angles

RECALL

1. The degree measure of a minor arc is the measure of the central angle which intercepts the arc.

2. The degree measure of a major arc is equal to 360 minus the measure of the minor arc

with the same endpoints.

3. The degree of the semicircle is 180.

IRA

Php. 1, 594,655,094.00

(64.62%)

Tax Revenue (Local and Property)

Php. 765, 233,114.32

(31.01%)

Operating and

Miscellaneous Revenue

Php. 102, 118,725.12

(4.14%)

Others

Php. 5, 800,745.39

(0.24%)

Guide Questions:

1. Which item did Cavite province get the most of its income? Explain.

2. In which item did Cavite province get the least of its income?

3. In the circle graph, what is the measure of the central angle corresponding to each item?

4. How is the measure of the central angle corresponding to each item determined?

Let's do more!

Challenge yourself!

Check-Up!

Were you able to measure the central angles and arcs? I’m sure you did! Well done!

➢> The sum of the measures of the central

angles of a circle with no common interior

points is 360 degrees.

➢> The degree measure of an arc is the

measure of the central angle which

intercepts the arc.

Did you know that the capital of the province of Cavite is Trece Martirez City. Based on the map, which town is directly to the north of Trece Martirez? How about to the east of it? West? Which town is directly to the south of Trece Martirez?

C. ABSTRACTION

Activity 2: Measure Me and You will Know…

APPLICATION

Study the circle graph and answer the questions that follow

Figure is taken from Cavite Socio-Economic and Physical Profile 2012

Check-Up!

Did you measure the angles accurately and

find the sum of their measures?

Did you find the relationship between the measures of the central angle and its intercepted arc? I know you did! The next activities will be more fun because we are going to find out how circles are illustrated in real-life situations.

1. If the point of the spinner is moved from A to B,

what is the measure of the angle formed by the spinner and the positive y- axis?

Activity 2:

Measure Me and You will Know…

Let’s think about this!

1. If the point of the spinner is moved from A to B,

what is the measure of the angle formed by the spinner

and the positive y- axis?

Activity 1:

Spin Me all Over Cavite!

A spinner has been placed over the map of the province of Cavite placed in the coordinate plane. Investigate the point of the spinner when moved from point A to D and intuitively measure the angle formed by the spinner. Answer the guide questions on the Analysis.

Are you ready? Here’s the map!

Definitions:

Sum of Central Angles

The sum of the measures of the central angles

of a circle with no common interior points is

360 degrees.

A

5. What kind of figure has the spinner point traced from A through D clockwise?

B

D

4 1

3 2

4. What is the sum of the measures of all four angles?

Would this answer be different if the spinner were1 cm longer?

1 cm shorter?

3. The spinner point is moved clockwise from C to A. What is the sum of the measures of angles 3 and 4?

1. If the point of the

spinner is moved

from A to B,

what is the measure of

the angle formed by the spinner and the

positive y- axis?

C

2. If the point is then moved to C, what is the measure of the angle formed by the spinner and the positive x- axis?

Degree Measure of an Arc

Activity 2: Measure Me and You will Know…

Did you enjoy the first activity? Now let’s gear up for a more challenging one. Here, you will use your skill in measuring angles using a protractor. After you measure the angles of the figure below and tabulated all their measurements you will know what this is all about.

Let's sum it up

Did you know that the national government subsidy is in the form of Internal Revenue Allotment or what is commonly known as IRA. Yes! The national government give every local government the fund resources so that all LGU’s (Local Government Units) can function to provide necessary programs for its constitutients- that means US.

“The income of the province is very important in defining the programs to be implemented under the local administration, social and economic sectors. The source of income of the province can come from national government subsidy, local collections and other sources, being the first two as the foremost resource” (Cavite Socio-Economic and Physical Profile 2012).

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