Math Destroyer Test 2 # 27

[PocketRocket]

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27. In the circle below angle ABD is formed by tangent line AB and secant BD. If arc AC on the circle subtends an angle of 30 degrees and arc AD subtends an angle of 100 degrees, find the measure of the angle ABD.

A. 70 degrees
B. 65
C. 35
D. 60
E. 50

The answer is C

In the explanation they are using "Angle formed outside"=(1/2)x(difference of the intercepted arcs) because its

What do they mean by "intercepted arcs"? and why are they taking the difference?

 

[DAT Destroyer]

27. In the circle below angle ABD is formed by tangent line AB and secant BD. If arc AC on the circle subtends an angle of 30 degrees and arc AD subtends an angle of 100 degrees, find the measure of the angle ABD.

A. 70 degrees
B. 65
C. 35
D. 60
E. 50

The answer is C

In the explanation they are using "Angle formed outside"=(1/2)x(difference of the intercepted arcs) because its

What do they mean by "intercepted arcs"? and why are they taking the difference?View attachment 190522

An intercepted arc is the arc that is formed when segments intersect portions of a circle and create arcs. 2 arcs can be formed by either 2 secant lines, a secant and a tangent ( like the problem you posted) or 2 tangents. In all 3 cases to find the measure of the angle you subtract the angle subtended by the small are from the angle subtended by the large arc and you divide the result by 2.

There's a proof but you won't need it for DAT.

 

[PocketRocket]

The arc that's 100 degrees, AD, is the arc on the left side of the circle OR the right side of the circle overlapping the AC arc?

 

[DAT Destroyer]

The left side of the circle

 

[PocketRocket]

Ohhhh ok makes sense! thank you orgoman22!!

 

[DAT Destroyer]

Ohhhh ok makes sense! thank you orgoman22!!

You are welcome.

Good luck in your studies and on the DAT

Nancy

 

[whiteoaks123]

Can someone please explain what this question is even asking? What does it mean by arc AC subtends and angle of 30 and arcAD subtends 100?

 

[DAT Destroyer]

Can someone please explain what this question is even asking? What does it mean by arc AC subtends and angle of 30 and arcAD subtends 100?

When we say an arc subtends an angle, we are interested in the measure of the angle whose sides cut through an arc on the circle.

If the vertex of the angle is at the center of the circle, the measure of the angle is the same as the measure of the arc. The other case is when the vertex of the angle is at the circumference of the circle. The third case is the one shown in the above problem, where the vertex of the angle is outside the circle.

Hope this helps!