find m<DCB given angles A and F are congruent, angles B and E are congruent and m<CDE = 26
To find the measure of angle <DCB, we can use the fact that the sum of the measures of angles in a triangle is 180 degrees.
In this case, we can start by identifying the angles that are congruent. We are given that angles A and F are congruent, and angles B and E are congruent.
Since the sum of the measures of angles A, B, and C is 180 degrees, and angles A and B are congruent, we can express the measure of angle C as 180 - 2A.
Similarly, since the sum of the measures of angles D, E, and F is 180 degrees, and angles E and F are congruent, we can express the measure of angle D as 180 - 2E.
Now, we are given that m<CDE = 26. This means that angle CDE measures 26 degrees.
To find angle D, we can substitute the given values into the equation for angle D:
180 - 2E = 26
Solving this equation for E:
2E = 180 - 26
2E = 154
E = 154/2
E = 77
Now that we know E = 77, we can substitute it into the equation for angle D:
D = 180 - 2E
D = 180 - 2(77)
D = 180 - 154
D = 26
Therefore, angle D measures 26 degrees.
To find angle C, we can substitute the values of angles A and D into the equation for angle C:
C = 180 - 2A
C = 180 - 2(26)
C = 180 - 52
C = 128
Therefore, angle C measures 128 degrees.
Finally, to find angle <DCB, we subtract the measures of angles D and C from 180 degrees:
<DCB = 180 - (D + C)
<DCB = 180 - (26 + 128)
<DCB = 180 - 154
<DCB = 26
Therefore, angle <DCB measures 26 degrees.