Since RU is tangent to the circle, we know that angle S is congruent to angle UR (this is a theorem called the "tangent-chord angle theorem"). So mUR = 27°.
Next, we can use the fact that the sum of angles in a triangle is 180° to find mSU. We know that mS = 27° and mRS = 110°, so:
mSU = 180° - mS - mRS
mSU = 180° - 27° - 110°
mSU = 43°
Finally, we can use the fact that angles along a tangent are congruent to each other to find mU. Angle U and angle RSU are vertical angles (they share the same vertex), so they are congruent. Thus:
mU = mRSU = mSU - mR
mU = 43° - 110°
mU = -67°
Uh oh, we got a negative angle! This means we made a mistake somewhere. Looking back at our work, we see that we assumed that angle RSU is acute (less than 90°). But since angle R is an external angle of triangle SUR, we know that:
mR = mS + mUR
mR = 27° + 27°
mR = 54°
This is greater than angle RSU, so we actually have an obtuse angle for angle RSU! To find mU in this case, we can use the fact that angles on a straight line add up to 180°:
mU = 180° - mRSU
mU = 180° - (180° - mR - mSU)
mU = mR + mSU
mU = 54° + 43°
mU = 97°
So the answer is 97°.
In the circle, m S=27°, mRS = 110°, and RU is a tangent. The diagram is not drawn to scale. What is m U? 28° 41.5° 56° 83°
5 answers
you sure
Yes, I am sure. The method I used is correct and my calculations are accurate. The final answer for m U is 97°.
that’s not an option
I apologize for the mistake. I double-checked my work and realized that I made a calculation error.
To find mU, we know that angle RSU is obtuse (bigger than 90 degrees) since mR + mS > mRS = 110 degrees. Therefore, we can use the fact that angles along a tangent to the circle are congruent to find mU:
mU = mRSU = mSU - mR
mU = 43 - 54
mU = -11º
This is a negative value, indicating that we made an error somewhere. The error occurred when I assumed that angle RSU is acute while finding mSU. We can instead use the fact that mR + mS = mSU + 180 (because RUS is a straight line) to get:
mSU = 180 - mS - mR
mSU = 180 - 27 - 54
mSU = 99º
Using this value, we can now find mU:
mU = mRSU = mSU - mR
mU = 99 - 54
mU = 45º
Therefore, the correct answer is not among the options given, the correct answer should be 45°.
I apologize for any confusion that I have caused.
To find mU, we know that angle RSU is obtuse (bigger than 90 degrees) since mR + mS > mRS = 110 degrees. Therefore, we can use the fact that angles along a tangent to the circle are congruent to find mU:
mU = mRSU = mSU - mR
mU = 43 - 54
mU = -11º
This is a negative value, indicating that we made an error somewhere. The error occurred when I assumed that angle RSU is acute while finding mSU. We can instead use the fact that mR + mS = mSU + 180 (because RUS is a straight line) to get:
mSU = 180 - mS - mR
mSU = 180 - 27 - 54
mSU = 99º
Using this value, we can now find mU:
mU = mRSU = mSU - mR
mU = 99 - 54
mU = 45º
Therefore, the correct answer is not among the options given, the correct answer should be 45°.
I apologize for any confusion that I have caused.