None of the above, it's a hard one alright!
Answer:
(d) m∠AEB = m∠ADB
Step-by-step explanation:
The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.
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<h3>applicable relations</h3>
Several relations are involved here.
- The measures of the arcs of a circle total 360°
- A diameter cuts a circle into two congruent semicircles
- The measure of an inscribed angle is half the measure of the arc it intercepts
<h3>application</h3>
In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)
If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.
The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.
m∠AEB = m∠ADB
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<em>Additional comment</em>
Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.
Answer:
16
Step-by-step explanation:
Answer:
16a+20
Step-by-step explanation:
Distribution property
4×4a + 4×5
16a. + 20
The spinner is not shown, so I will explain you the procedure with a spinner that is used in a problem with same statement, but different questions.
This explanation will suffice you even if the spinner is different, because you will know how to solve the problem.
The characteristics of the spinner are:
- circular board
- 8 congruent segments
- the segments are numbered 1, 2, 3, 4, 5, 6, 7, and 8
As conclusion, each segment (number) has the same change to be the outcome.
a) P (factor of 42). This is to find the probability that the outcome is a number that is factor of 42.
Then analyze the possible outcomes:
1: yes (1*42 = 42)
2: yes (2*21 = 42)
3: yes (3*14 = 42)
4: no
5: no
6: yes (6*7 = 42)
7: yes (7*6 = 42)
8 no.
Then five of the possibilities out of 8 are factor of 42, and P (factor of 42) = 5/8
Answer: 5/8
b) P (multiple of 6)
The only multiple of 6 in the numbers 1 through 8 is 6.
Then the P (multiple of 6) is 1/8
Answer: 1/8