Given:
[tex]m \angle A B D=96^{\circ}[/tex]
[tex]m \angle 2 =m \angle 1+ 26^{\circ}[/tex]
To find:
[tex]m \angle 1[/tex]
Solution:
[tex]m \angle DBC+ m \angle CBA = m \angle ABD[/tex]
[tex]m \angle 1+ m \angle 2 = m \angle ABD[/tex]
Substitute [tex]m \angle 2 =m \angle 1+ 26^{\circ}[/tex].
[tex]m \angle 1+ m \angle 1 + 26^\circ = 96^\circ[/tex]
[tex]2m \angle 1+ 26^\circ = 96^\circ[/tex]
Subtract 26° from both sides.
[tex]2m \angle 1+ 26^\circ -26^\circ = 96^\circ -26^\circ[/tex]
[tex]2m \angle 1 = 70^\circ[/tex]
Divide by 2 on both sides, we get
[tex]m \angle 1=35^{\circ}[/tex]
Therefore, m∠1 = 35°.
