Answer:
m∠ADB = 36
Explanation:
Pre-Solving
We are given parallelogram ABCD.
We know that DB is a diagonal in the parallelogram.
We also know that m∠A = 115 degrees and m∠BDC = 29 degrees.
We want to find m∠ABD.
Recall that a parallelogram has two pairs of parallel sides; this means that AB is parallel to DC and AD is parallel to BC.
We can treat AD is a transversal between AB and DC, because it is intersecting those lines at different points.
Solving
So, AD is a transversal - recall that same-side interior angles of a transversal are supplementary, meaning they add up to 180 degrees.
This means that m∠A + m∠D = 180
If we look at the diagram, we can see that m∠D is consisted of m∠BDC and m∠ADB, meaning that we can substitute m∠D for m∠BDC + m∠ADB.
We get:
m∠A + m∠BDC + m∠ADB = 180
We can substitute the values that we know into the equation:
115 + 29 + m∠ADB = 180
144 + m∠ADB = 180
m∠ADB = 36