The measure of angle A is 65°
Explanation:
Given that ABCD is a quadrilateral inscribed in a circle.
The measure of angle A is [tex]\angle A=(2x+1)^{\circ}[/tex]
The measure of angle B is [tex]\angle B=148^{\circ}[/tex]
The measure of angle D is [tex]\angle D=x^{\circ}[/tex]
We need to determine the measure of angle A.
Since, we know that the angles B and D are opposite angles and the opposite angles of a quadrilateral add up to 180°
Thus, we have,
[tex]\angle B+\angle D=180^{\circ}[/tex]
Substituting the values, we have,
[tex]148^{\circ}+x=180^{\circ}[/tex]
[tex]x=32^{\circ}[/tex]
Thus, the value of x is 32°
Substituting the value of x in the measure of angle A, we get,
[tex]\angle A=(2x+1)^{\circ}[/tex]
[tex]\angle A=(2(32)+1)^{\circ}[/tex]
[tex]\angle A=(64+1)^{\circ}[/tex]
[tex]\angle A=65^{\circ}[/tex]
Thus, the measure of angle A is 65°
