Answer:
x=5
∠ABD = 33
∠A = 115
Step-by-step explanation:
Once again here are the properties of a trapezoid:
Opposite angles are congruent
Opposite side lengths are congruent
And here is a property of a triangle:
the measure of the angles add up to equal 180
Given this information we need to find
x, ∠ABD and ∠A
First lets find x
Remember opposite side lengths are congruent
Segment AD and segment BC are opposite side lengths ( which are congruent)
That being said we create an equation to solve for x
2x = 10
step 1 divide each side by 2
2x/2=x
10/2=5
we're left with x = 5
Now lets find ∠A
∠C and ∠A are opposite angles
so ∠C≅∠A
Because ∠C = 115 ∠A also = 115
Finally lets find ∠ABD
because ∠BDC and ∠ABD are opposite angles we can find the measure of ∠BDC and get the value of ∠ABD
ΔBDC is a triangle formed within the parallelogram
That being said we can find the measure of ∠BDC using the triangle angle rule (stated previously)
That the measures of the angles in a triangle add up to equal 180
So we can find the missing angle (∠BDC) by subtracting the given angles ( which have a measure of 32 and 115) from 180
∠BDC = 180 - 32 - 115
180 - 32 - 115 = 33
so ∠BDC = 33
Meaning that ∠ABD also = 33
