Question

4. Based on the labeled triangle below, complete the paragraph below: 5 SABC, ADB + AABC, AD BC Given that mZ3+ m25=m/DAB is true because of the postulate. The linear pair postulate shows that the mZDAB=180. The property lets m24+ m23+ m25 = 180° The Alternate Interior Angle Theorem shows that 212 and 25. This means m21= m24, mZ2= m25 by the Definition of Through the mZ1+ m2 + m3= 180° proving the Triangle Sum Angle Theorem. ​

Answer 1

The missing angle in triangle DAB is 55°.

Step-by-step explanation:

In triangle DAB, we know that the sum of all angles is 180° according to the Triangle Sum Angle Theorem. Given that m∠3 + m∠25 = m∠DAB, and the linear pair postulate shows that m∠DAB = 180°, we can calculate m∠3 = 180° - m∠25. Substituting the value of m∠25 as 125°, we get m∠3 = 180° - 125° = 55°. Therefore, the missing angle in triangle DAB is 55°.

The Alternate Interior Angle Theorem states that when two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Applying this theorem, we find that m∠21 = m∠24 and m∠2 = m∠25. By using these relationships and the properties of angles in triangles, we can accurately determine the missing angle in triangle DAB.

The calculations and deductions made above provide a clear understanding of how the missing angle in triangle DAB is determined. By applying the relevant postulates and theorems, we can confidently conclude that the measure of angle DAB is indeed 55°.