In triangle ABC , angle A = 50 deg angle B = 30 deg and angle C = 100 deg .What are the angles of the triangle formedby joining the midpoints of the sides of thistriangle?
To find the angles of the triangle formed by joining the midpoints of the sides of triangle ABC, we can use the fact that connecting the midpoints of the sides creates a triangle known as the "midsegment triangle." The midsegment triangle is similar to the original triangle, and its angles can be found using the following relationships:
1. The angle opposite the midpoint of a side in the midsegment triangle is half the measure of the angle opposite that side in the original triangle.
2. The angle opposite the side connecting two midpoints in the midsegment triangle is supplementary to the angle opposite the third side in the original triangle.
Now, let's apply these relationships to triangle ABC:
1. Angle A' (opposite the midpoint of side BC) = 0.5 * angle A = 0.5 * 50° = 25°
2. Angle B' (opposite the midpoint of side AC) = 0.5 * angle B = 0.5 * 30° = 15°
3. Angle C' (opposite the midpoint of side AB) = 0.5 * angle C = 0.5 * 100° = 50°
So, the angles of the triangle formed by joining the midpoints of the sides of triangle ABC are as follows:
Answers & Comments
Answer:
To find the angles of the triangle formed by joining the midpoints of the sides of triangle ABC, we can use the fact that connecting the midpoints of the sides creates a triangle known as the "midsegment triangle." The midsegment triangle is similar to the original triangle, and its angles can be found using the following relationships:
1. The angle opposite the midpoint of a side in the midsegment triangle is half the measure of the angle opposite that side in the original triangle.
2. The angle opposite the side connecting two midpoints in the midsegment triangle is supplementary to the angle opposite the third side in the original triangle.
Now, let's apply these relationships to triangle ABC:
1. Angle A' (opposite the midpoint of side BC) = 0.5 * angle A = 0.5 * 50° = 25°
2. Angle B' (opposite the midpoint of side AC) = 0.5 * angle B = 0.5 * 30° = 15°
3. Angle C' (opposite the midpoint of side AB) = 0.5 * angle C = 0.5 * 100° = 50°
So, the angles of the triangle formed by joining the midpoints of the sides of triangle ABC are as follows:
Angle A' = 25°
Angle B' = 15°
Angle C' = 50°
Answer:
Step-by-step explanation:
The correct option is C
30∘,40∘,110∘
In ΔABC,
∠A=30∘,∠B=40∘,∠C=110∘
D, E and F are mid -points of the sides of the triangle . By joining them in order, DEF is a triangle formed
Now BDEF, CDFE and AFDE are || gm
∴∠A=∠D=30∘
∠B=∠E=40∘
∠C=∠F=110
∴ Angles are 30∘,40∘,110∘