Respuesta :
Answer:the measure of angle E in triangle EFG is 69 degrees.
Step-by-step explanation:
AI-generated answer
Given that triangle EFG is shown with angle F as 42 degrees, side EF as 7 cm, and side EG as 7 cm, we can determine the measure of angle E using the properties of triangles.
In a triangle, the sum of all three angles is always 180 degrees. Since we know angle F is 42 degrees, and both sides EF and EG are equal (7 cm), this triangle is an isosceles triangle where the two equal sides are opposite the equal angles.
To find angle E:
1. Since EF and EG are equal sides, angles opposite these sides are also equal.
2. In an isosceles triangle, the base angles (angles opposite the equal sides) are equal.
3. Therefore, angle E = angle G.
Now, let's find angle E:
1. Angle F = 42 degrees
2. Angle E + Angle G + Angle F = 180 degrees (sum of angles in a triangle)
3. Angle E + Angle E + 42 = 180 (substitute angle G with angle E)
4. 2*Angle E = 180 - 42
5. 2*Angle E = 138
6. Angle E = 138 / 2
7. Angle E = 69 degrees
Therefore, the measure of angle E in triangle EFG is 69 degrees.
