5) find the measure of angle bdc.
6) find the measure of angle a.
7) find the value of x.
8) find the missing angle.

Question

Accepted Answer

### Problem 5: Find the measure of angle BDC
# Explanation:
## Step 1: Use the exterior angle theorem
The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle $BDC$, $\angle VBC$ is an exterior angle, so $20x + 5=(9x - 2)+40$
## Step 2: Solve for $x$
$$
\begin{align*}
20x+5&=9x - 2+40\
20x+5&=9x + 38\
20x-9x&=38 - 5\
11x&=33\
x&=3
\end{align*}
$$
## Step 3: Find the measure of $\angle BDC$
Substitute $x = 3$ into the expression for $\angle BDC$ which is $9x-2$
$\angle BDC=9\times3 - 2=27 - 2 = 25^{\circ}$

# Answer: $25^{\circ}$

### Problem 6: Find the measure of angle A
# Explanation:
## Step 1: Use the angle sum property of a right - triangle
In a right - triangle, the sum of the two non - right angles is $90^{\circ}$. So $(x + 37)+(x + 67)=90$
## Step 2: Solve for $x$
$$
\begin{align*}
x+37+x + 67&=90\
2x+104&=90\
2x&=90 - 104\
2x&=- 14\
x&=-7
\end{align*}
$$
## Step 3: Find the measure of $\angle A$
Substitute $x=-7$ into the expression for $\angle A$ which is $x + 37$
$\angle A=-7 + 37=30^{\circ}$

# Answer: $30^{\circ}$

### Problem 7: Find the value of $x$
# Explanation:
## Step 1: Use the angle sum property of a triangle
The sum of the interior angles of a triangle is $180^{\circ}$. So $(x + 8)+(2x-3)+(6x - 5)=180$
## Step 2: Solve for $x$
$$
\begin{align*}
x + 8+2x-3+6x - 5&=180\
( x+2x + 6x)+(8-3 - 5)&=180\
9x+0&=180\
x&=20
\end{align*}
$$

# Answer: $x = 20$

### Problem 8: Find the missing angle
# Explanation:
## Step 1: Identify the relationship between angles
First, the angle opposite to $35^{\circ}$ (vertical angles) is also $35^{\circ}$. Then, in the triangle, we know one angle is $100^{\circ}$ and another is $35^{\circ}$. Let the missing angle of the triangle be $y$, then $y=180-(100 + 35)=45^{\circ}$. The angle we need to find is supplementary to $y$, so the missing angle $=180 - 45=135^{\circ}$ (or we can use the exterior angle property: the missing angle $=100 + 35=135^{\circ}$)

# Answer: $135^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Problem 5: Find the measure of angle BDC

Step 1: Use the exterior angle theorem

Step 2: Solve for \(x\)

Step 3: Find the measure of \(\angle BDC\)

Step 1: Use the angle sum property of a right - triangle

Step 2: Solve for \(x\)

Step 3: Find the measure of \(\angle A\)

Step 1: Use the angle sum property of a triangle

Step 2: Solve for \(x\)

Answer:

Problem 6: Find the measure of angle A