Question

in the given figure, PAT is tangent at A.
If angle ACB = 50°, find (i) angle TAB (ii) angle ADB.​

Answer 1

$= > tab = 50$

adb

$= > adb = 130$

Answer 2

Given:

Angle ACB=50°

To find:
(i) angle TAB

(ii) angle ADB

Solution:

The measure of angle TAB is 50° and angle ADB is 130°.

(i) The given line PAT is tangent to the circle and so the angle in the alternate segment of the ΔABC will be equal to the angle TAB.

So, angle TAB=angle ACB

Angle TAB=50°

(ii) Now, the quadrilateral ADBC is cyclic and the sum of angles opposite to each other will be 180°.

Angle ADB+angle ACB=180°

Using values,

Angle ADB+50°=180°

Angle ADB=180°-50°

Angle ADB=130°

Therefore, the required measure of angle TAB is 50° and angle ADB is 130°.