Question

Drag a statement or reason to each box to complete this proof. given: the measure of angle a b d equals 60 degrees. the measure of angle d b c equals 40 degrees. prove: triangle a b c is an obtuse triangle. art: triangle a b c with horizontal base b c is drawn. a bisector b d is drawn on a c. the bisector divides a c into two parts a d and d c. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. statements reasons

1. m∠abd=60°, m∠dbc=40° given
2. m∠abd m∠dbc=m∠abc response area
3. response area substitution property of equality
4. response area simplifying
5. ∠abc is an obtuse angle. response area
6. △abc is an obtuse triangle. definition of obtuse triangle

Answer 1

To prove that triangle ABC is obtuse, we sum the measures of angles ABD and DBC which gives us angle ABC measuring 100°, indicating that the triangle is obtuse.

Step-by-step explanation:

Given the measures of angles in the triangle, we will prove that triangle ABC is an obtuse triangle step by step. The given information states that m∠ABD = 60° and m∠DBC = 40°.

1. m∠ABD = 60°, m∠DBC = 40°: Given by the problem.
2. m∠ABD + m∠DBC = m∠ABC: By the angle addition postulate, angles ABD and DBC are adjacent, thus their sum is equal to angle ABC.
3. m∠ABC = 100°: By substituting the given values for m∠ABD and m∠DBC and simplifying (60° + 40°).
4. ∠ABC is an obtuse angle because it measures more than 90° but less than 180°.
5. Since ∠ABC is obtuse, by the definition of an obtuse triangle, triangle ABC is classified as an obtuse triangle because it contains one obtuse angle.