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We have been given a diagram. We are asked find the measure of arc EAB.
First of all, we will find the measure of arcs ED and CB using our given information.
We know that measure of an inscribed angle is half the measure of intercepted arc.
We can see that angle EBC is inscribed angle of arc EDC, so measure of arc EDC will be twice the measure of angle EBC.
Similarly, we will find the measure of arc DCB.
Therefore, the measure of arc EAB is 148 degrees and option C is the correct choice.
Answer:
Therefore.
angle 1 is congruent to angle 3 ...Proved
The proof with steps are below with Fill in the blanks
Step-by-step explanation:
Complementary Angles:
Two angles are Complementary when they add up to 90 degrees.
Example 40° and 50° are Complementary Angles.
If 'x' and 'y' are Complementary Angles the we have
Here,
Given:
angle 1 and angle 2 are complementary
angle 3 and angle 2 are complementary
To Prove:
angle 1 is congruent to angle 3
Proof:
Step 1:
angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.
Step 2:
By the definition of complementary angles,
m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.
Step 3:
Transitive Property of Equality.
Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.
Step 4:
Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get
m of angle 1 = _measure of angle_3_.
Step 5:
Angles with the same measure are _Congruent__,
Step 6:
so angle 1 is congruent to angle 3.
Therefore.
angle 1 is congruent to angle 3 ...Proved