Given: ΔABC, m∠1=m∠2, D∈
AC, BD = DC
m∠BDC = 100º
Find: m∠A
m∠B, m∠C
No they are the angles that line BD form from angle B
We are given that ΔABC is a triangle, m∠1 is equal to m∠2, D is a point on AC, BD is equal to DC, and m∠BDC is equal to 100º.
To find the measures of angles A, B, and C, we can use the fact that the sum of angles in a triangle is equal to 180 degrees.
Step 1: Find m∠B
Since BD is equal to DC, we can conclude that m∠BDC is equal to m∠BCD. Therefore,
m∠B + m∠BCD + m∠BDC = 180º
m∠B + m∠BDC + m∠BDC = 180º (Since m∠BDC = m∠BCD)
m∠B + 2m∠BDC = 180º
We are given that m∠BDC is equal to 100º. Substituting this value, we have:
m∠B + 2(100º) = 180º
m∠B + 200º = 180º
m∠B = 180º - 200º
m∠B = -20º
However, angles cannot have negative measures. Therefore, there must be an error in the given information or question.
Since there is an error, we cannot proceed to find the measures of angles A and C. Please re-check the given information or provide more details.
To find the measures of angles A, B, and C in triangle ABC, we can use the properties of triangles and angles.
1. Use the Angle Sum Property of a Triangle:
The Angle Sum Property of a Triangle states that the sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
∠A + ∠B + ∠C = 180
2. Use the given information to find ∠C:
From the given information, we know that ∠BDC = 100 degrees.
Since ∠BDC is an exterior angle of triangle ABC, it is equal to the sum of the two opposite interior angles, ∠BDA and ∠C. Therefore,
∠BDC = ∠BDA + ∠C
Substituting the known value, we get:
100 = ∠BDA + ∠C
3. Use the given information to find ∠BDA:
From the given information, we know that BD = DC, and m∠1 = m∠2. Also, we can deduce that m∠ABC = m∠ACB since they are opposite angles of an isosceles triangle.
Since BD = DC, triangle BDC is an isosceles triangle. This means that ∠C is congruent to ∠BDC.
Furthermore, ∠BDC and ∠C are corresponding angles, so they are also congruent. Therefore,
∠C = ∠BDC = 100 degrees
Since ∠BDC = ∠C = 100 degrees, we can find ∠BDA as follows:
∠BDA = 180 - (∠BDC + ∠C)
∠BDA = 180 - (100 + 100)
∠BDA = 180 - 200
∠BDA = -20 degrees
4. Substitute the values of ∠BDA and ∠C into the equation:
Using the values we have found for ∠BDA (-20 degrees) and ∠C (100 degrees), we can substitute them into the equation from step 2:
100 = ∠BDA + ∠C
100 = -20 + 100
100 = 80
This equation does not hold true, which means there is no solution that satisfies the given conditions.
Therefore, based on the given information, we cannot determine the measures of ∠A, ∠B, and ∠C in triangle ABC.
what are ∠1 and ∠2?
∠A, ∠B ?