Please help!! need help ASAP please!!

Question

Question 1: Find the value of the indicated angles.

A.) 43°

B.) 39°

C.) 35°

D.) 41°

Question 2: A designer creates a circular ornament as shown. Identify m∠ADB.

A.) m∠ADB = 110°

B.) m∠ADB = 100°

C.) m∠ADB = 95°

D.) m∠ADB = 105°

Please give the explanations and answers as soon as possible please!

Answer 1

Question 1:

Both angles create the same intercepted arc on the circle. This means that both angles are equal to each other. Setting 8b - 1 = 6b + 9 allows you to algebraically solve for b, which equals 5. Plugging this value in to both angle expressions gives you an angle measure of 39 degrees, so the answer is B.

Question 2:

To find the measure of angle ADB, you first need to acknowledge that it is part of triangle ADB, with angle ABD already specified as 30 degrees. This means that if we can find the measure of angle BAD, we can find the third remaining angle (ADB), knowing that all three angles add up to 180 degrees. Angle BAD is an inscribed angle that creates an intercepted arc with a measure of 110 degrees. This means that angle BAD is going to be half of this arc (55 degrees). We now know that triangle ADB has two angles of 30 degrees and 55 degrees, which add up to 85 degrees. Subtracting this from 180 degrees and we can see that the remaining angle ADB is 95 degrees, so the answer is C.

Answer 2

Becky,

For question (1), both inscribed angles intercept the same arc. This means 8*b-1=6*b+9 solve for b and plug in this value to find the answer.