Triangle ABC is similar to triangle FGH. Angle A measures 42 degrees. Angle B measures 19 degrees. Find the measure of angle H.
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,
\(\triangle ABC\sim \triangle FGH\)
By the above statement,
\(m\angle A=m\angle F\)
\(m\angle B=m\angle G\)
\(m\angle C=m\angle H\)
We have,
\(m\angle A=42^{\circ}\) and \(m\angle B=19^{\circ}\)
Since, \(m\angle A+m\angle B+m\angle C = 180^{\circ}\)
\(\implies m\angle C=180^{\circ}-m\angle A - m\angle B=180^{\circ}-42^{\circ}-19^{\circ}=119^{\circ}\)
\(\implies m\angle H=119^{\circ}\)
Hence, the measure of the angle H is 119°.