HELP PLEASE , i need it asap

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

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