The measure of angle A is 42°
Explanation:
Given that ABCD is a quadrilateral.
The measures of angles are [tex]\angle A=x+5[/tex], [tex]\angle B= 2x[/tex] and [tex]\angle D=3x-5[/tex]
We need to determine the measure of angle A
The value of x:
Since, we know that 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 get,
[tex]2x+3x-5=180^{\circ}[/tex]
[tex]5x-5=180[/tex]
[tex]5x=185[/tex]
[tex]x=37[/tex]
Thus, the value of x is 37
Measure of [tex]\angle A[/tex]:
The measure of angle A can be determined by substituting [tex]x=37[/tex] in [tex]\angle A=x+5[/tex], we get,
[tex]\angle A=37+5[/tex]
[tex]\angle A=42^{\circ}[/tex]
Thus, the measure of angle A is 42°
