Questions: What is the value of x in the figure shown below?
Transcript text: What is the value of $x$ in the figure shown below?
Solution
Solution Steps
Step 1: Analyze the given figure
We are given a parallelogram ABCD with AB=CD=4.3 and AC=BD=3. Also, we are given ∠DAB=69∘ and ∠ABC=43∘+x∘. We need to find the value of x.
Step 2: Properties of a parallelogram
In a parallelogram, opposite angles are equal. Thus, ∠DAB=∠DCB=69∘ and ∠ABC=∠ADC.
Also, adjacent angles are supplementary, which means their sum is 180∘. Therefore, ∠DAB+∠ABC=180∘.
Step 3: Calculate the value of x
We have ∠DAB+∠ABC=180∘.
69∘+(43∘+x∘)=180∘69∘+43∘+x∘=180∘112∘+x∘=180∘x∘=180∘−112∘x∘=68∘