### Geometry Problem: Angle Calculation#### Question 5Given the figure below with $ m\angle BFA = 166^\circ $ and $ m\angle BD = 88^\circ $, what is $ m\angle BDA $?![Diagram illustrating the geometric shapes and angles involved](image URL)#### Explanation of the Diagram:The diagram provided is a geometric sketch consisting of a circle with various lines intersecting it. Here is a detailed description:- Points $ A $, $ B $, $ D $, and $ E $ are marked on the figure.- A circle passes through points $ A $, $ C $, and $ D $.- Line segments $ BA $ and $ BE $ are extended to meet the circle at points $ A $ and another unmarked point on the opposite side of the circle.- $ F $ is a point such that $ BFA $ forms an external angle with the circle and the line extended through the circle.- $ \angle BFA = 166^\circ $.- A line segment extends from $ B $ to $ D $, with $ m\angle BD = 88^\circ $.#### Answer Choices:- **A**: $ 39^\circ $- **B**: $ 83^\circ $#### Determine $ m\angle BDA $:To find $ m\angle BDA $:Given:\[ m\angle BFA = 166^\circ \]\[ m\angle BD = 88^\circ \]Using these angles, we can calculate $ m\angle BDA $ by considering the supplementary angles and the properties of angles within and outside the circle. The steps involve geometric reasoning about the circle's internal and external angles formed by intersecting lines:\[ m\angle BDA = 180^\circ - m\angle BD - m\angle BFA \]Insert the known values to find $ m\angle BDA $:1. **Calculate angle $ m\angle DBA $** (considering supplementary angles):\[ m\angle DBA = 180^\circ - m\angle BD \]\[ m\angle DBA = 180^\circ - 88^\circ \]\[ m\angle DBA = 92^\circ \]Since $ m\angle BFA $ is an external angle formed with the extension of the circle's chord, we subtract

Answered: Image /qna-images/answer/b4cee5b7-a496-49cb-9e64-d60f187c7d43.jpg

Answered: Given the figure below with mBFA = 166°…

Given the figure below with mBFA = 166° and mBD=88°, what is mZBDA? B F E D C

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter1: The Six Trigonometric Functions

Section1.2: The Rectangular Coordinate System

Problem 90PS: Draw 60 in standard position. Then find b if the point (2, b) is on the terminal side of 60.

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