. In Figure 5.17 to the right ABCD is a rectangle. If m(∠BDC) = 54, then find m(∠ABD) and m(∠CBD).
well, 54+36 = 90
ABCD is a parallelogram in which ,<ABD=400 and <ADC= 880. Find the measure of the angles <ADB and < DBC.
in figure 5.7 to the right ABCD is a rectangle.If m(<BDC)54
X+54=90
X=36
<B=x+54
<B=90
what is exactly the answer for the question then?
To find the measures of angles ∠ABD and ∠CBD, we need to use the properties of a rectangle.
First, we can deduce that opposite angles in a rectangle are congruent. This means that angles ∠ABD and ∠DCB are equal. Since we know that ∠BDC has a measure of 54 degrees, we can conclude that ∠DCB also has a measure of 54 degrees.
Now, we can use the fact that the sum of the interior angles of a triangle is 180 degrees. In triangle ABD, we have angles ∠ABD, ∠ADB, and ∠BDA. Since the sum of these angles must be 180 degrees, we can write the equation:
∠ABD + ∠ADB + ∠BDA = 180
Since ∠ADB is a right angle (90 degrees) in a rectangle, we can substitute this value into the equation:
∠ABD + 90 + ∠BDA = 180
Rearranging the terms, we get:
∠ABD + ∠BDA = 90
Since ∠ABD and ∠BDA are adjacent angles in a rectangle, they are supplementary (their sum is 180 degrees). Therefore, we can conclude that:
∠ABD = 180 - ∠BDA
Substituting this back into the equation, we get:
180 - ∠BDA + ∠BDA = 90
Simplifying, we find:
180 = 90
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