TA is a tangent at A. If < BCA=40° and < DAT=52°, find < BAD
Pls help me solve the question
To solve this question, we can use the fact that the angle between a tangent and a radius is 90 degrees. Here's how we can determine <BAD.
1. Start by drawing a diagram with the information given. Label points A, B, C, and D as indicated. Draw a line TA as the tangent to the circle at point A.
<pre>
C
/
/
/
A /______
| /
| /
T | /
| /
| / D
| /
|/
B
</pre>
2. From the given information, mark <BCA as 40 degrees and <DAT as 52 degrees. You can label these angles on the diagram.
<pre>
C
/|
/ |
/ |
A /____|__
| /
| BCA=40°
T | /
| /
| / D
| /
|/
B
</pre>
3. Remember that the angle between a tangent and a radius is always 90 degrees. Since TA is a tangent at point A, <BAT is a right angle of 90 degrees. Mark this angle on the diagram.
<pre>
C
/|
/ |
/ |
A /___|_50°_
| /
| /
T | /
|/
| 52°
B
</pre>
4. Use the fact that the sum of angles in a triangle is 180 degrees to find the remaining angles. In triangle ABD, we know that <BAT + <BAD + <DAB = 180 degrees. Given that <BAT is 90 degrees and <DAB is 50 degrees, we can substitute these values into the equation to solve for <BAD.
90 degrees + <BAD + 50 degrees = 180 degrees
Subtracting 140 degrees from both sides of the equation gives:
<BAD = 180 degrees - 140 degrees
Therefore, <BAD = 40 degrees.
5. So, <BAD is 40 degrees.