Question

Geometry! Please help!

DB¯¯¯¯¯ is a diagonal of ​ parallelogram ABCD ​ .

What is the measure of ∠ADB?

Answer 1

Angle ADB= 40 degrees.
The triangle ADB is equal to 180 degrees. Subtract 180-105=75
Since vertical angles are always congruent angle ABD= 35 degrees.
So 75-35=40.
I hope this is what you’re looking for

Answer 2

Remark
The way to do this problem is to find ADC first and then subtract <BDC from it.

Argument
A parallelogram has the property of having consecutive angles = to 180 degrees. That means that <DAB + <ADC = 180

Since <DAB = 105o then <ADC = 180 - 105 = 75

However, <ADC = 75 and <BDC = 35
<ADC = <ADB + <BDC
75 = <ADB +35 Subtract 35 from both sides
75 - 35 = 40

<ADB = 40 Degrees <<<<<< Answer