In each of the following figure, O is the centre of the circle. Find the measure of each lettered angle.
Answers
Given :
A circle with centre O, AB as diameter and AC and BC as chords. Also, <CBA = 35°.
To find :
In the figure, we have to find the value of x (<CAB).
Solution :
In the circle with centre O and AB as diameter, ∆BCA is a right angled triangle with <C=90° because :
- Angle in a semircircle is a right angle.
Now, sum of all the angles in a triangle is 180°.
- <ACB + <CBA + <BAC = 180°
- 90° + 35° + x = 180°
- 125° + x = 180°
- x = 180° - 125°
- x = 55°
Therefore, in the following figure, x = 55°.
Given :
A circle with centre O, AB as diameter and AC and BC as chords. Also, <CBA = 35°.
To find :
In the figure, we have to find the value of x (<CAB).
Solution :
In the circle with centre O and AB as diameter, ∆BCA is a right angled triangle with <C=90° because :
Angle in a semircircle is a right angle.
Now, sum of all the angles in a triangle is 180°.
<ACB + <CBA + <BAC = 180°
90° + 35° + x = 180°
125° + x = 180°
x = 180° - 125°
x = 55°
Therefore, in the following figure, x = 55°.