Respuesta :
Answer:
The measure of the angle H is 119°.
Step-by-step explanation:
Since, when two triangles are similar then their all corresponding angles are congruent or equal in measure,
Given,
[tex]\triangle ABC\sim \triangle FGH[/tex]
By the above statement,
[tex]m\angle A=m\angle F[/tex]
[tex]m\angle B=m\angle G[/tex]
[tex]m\angle C=m\angle H[/tex]
We have,
[tex]m\angle A=42^{\circ}[/tex] and [tex]m\angle B=19^{\circ}[/tex]
Since, [tex]m\angle A+m\angle B+m\angle C = 180^{\circ}[/tex]
[tex]\implies m\angle C=180^{\circ}-m\angle A - m\angle B=180^{\circ}-42^{\circ}-19^{\circ}=119^{\circ}[/tex]
[tex]\implies m\angle H=119^{\circ}[/tex]
Hence, the measure of the angle H is 119°.
