3. The side BC of ABC is produced to a point D. The bisector of A meets the side BC in P. If ABC = 30°, ACD = 110°, find APC
Share
3. The side BC of ABC is produced to a point D. The bisector of A meets the side BC in P. If ABC = 30°, ACD = 110°, find APC
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
To find the measure of \(\angle APC\), we can use the Angle Bisector Theorem.
According to the Angle Bisector Theorem, in a triangle, if an angle bisector divides the opposite side into segments \(b\) and \(c\), then \( \frac{AB}{AC} = \frac{b}{c} \).
In triangle ABC, angle bisector AP divides side BC into segments BP and PC.
Using the Angle Bisector Theorem in triangle ABC:
\[ \frac{AB}{AC} = \frac{BP}{PC} \]
Given that \(\angle ABC = 30°\) and \(\angle ACD = 110°\), we can find \(\angle BCD\):
\[ \angle BCD = 180° - \angle ACD = 180° - 110° = 70° \]
Now, using the Exterior Angle Theorem in triangle ABC:
\[ \angle BCD = \angle ABC + \angle APC \]
\[ 70° = 30° + \angle APC \]
\[ \angle APC = 70° - 30° \]
\[ \angle APC = 40° \]
Therefore, \(\angle APC = 40°\).
Step-by-step explanation:
Step-by-step explanation:
dekh lo bhaiya simple sa question hai ..... ab brainlist bhi bana do apne bhai ko