Answer:
Option 2nd is correct
67°
Step-by-step explanation:
Given that:
In right △ABC with right angle B.
[tex]m \angle B = 90^{\circ}[/tex], m∠A=(3x−8)° and m∠C=(x−2)°.
We know that the sum of all the measures of a triangle is 180 degree
In triangle ABC
⇒[tex]m\angle A+ m\angle B+ m\angle C = 180^{\circ}[/tex]
Substitute the values we have;
[tex]3x-8+90^{\circ}+x-2 = 180^{\circ}[/tex]
Subtract 90 degree from both sides we have;
[tex]3x-8+x-2 = 90^{\circ}[/tex]
Combine like terms;
[tex]4x-10= 90^{\circ}[/tex]
Add 10 to both sides we have;
[tex]4x=100^{\circ}[/tex]
Divide both sides by 4 we have;
[tex]x=25^{\circ}[/tex]
then;
m∠A=(3(25)−8)° = (75-8)° = 67°
Therefore, the measure of angle A is, 67°
