Okay, I will solve for $x$. Here's the solution:

Task 1

First, we need to determine if the two triangles are similar. We can check if their angles are equal.

• Triangle $BCD$: Angles are $39^\circ$, $86^\circ$, and $55^\circ$.
• Triangle $EFG$: Angles are $39^\circ$, $86^\circ$, and $55^\circ$.

Since the angles of the two triangles are the same, the triangles are similar by the Angle-Angle-Angle (AAA) similarity criterion.

Task 2

Now that we know the triangles are similar, we can set up a proportion to find $x$. We need to match the corresponding sides.

• Side $BD$ corresponds to side $EG$
• Side $BC$ corresponds to side $EF$

So, we can set up the proportion:

$\frac{BD}{EG} = \frac{BC}{EF}$

Plugging in the given values:

$\frac{97}{x} = \frac{61}{15}$

Task 3

Now, we solve for $x$:

$x = \frac{97 \cdot 15}{61}$

$x = \frac{1455}{61}$

$x \approx 23.852459$

Rounding to the nearest tenth, we get:

$x \approx 23.9$

Answer:
$x \approx 23.9$

Okay, I will solve for $x$ in the second problem. Here's the solution:

Task 1

First, we need to determine if the two triangles are similar. We can check if their angles are equal.

• Triangle $RST$: Angles are $49^\circ$, $57^\circ$, and $74^\circ$.
• Triangle $UVW$: Angles are $49^\circ$, $57^\circ$, and $74^\circ$.

Since the angles of the two triangles are the same, the triangles are similar by the Angle-Angle-Angle (AAA) similarity criterion.

Task 2

Now that we know the triangles are similar, we can set up a proportion to find $x$. We need to match the corresponding sides.

• Side $RS$ corresponds to side $UV$
• Side $RT$ corresponds to side $UW$

So, we can set up the proportion:

$\frac{RS}{UV} = \frac{RT}{UW}$

Plugging in the given values:

$\frac{83}{37} = \frac{91}{x}$

Task 3

Now, we solve for $x$:

$x = \frac{91 \cdot 37}{83}$

$x = \frac{3367}{83}$

$x \approx 40.566265$

Rounding to the nearest tenth, we get:

$x \approx 40.6$

Answer:
$x \approx 40.6$

Okay! I see three problems. I will solve for $x$ in the third problem. Here's the solution:

Task 1

First, we need to determine if the two triangles are similar. We can check if their angles are equal.

• Triangle $PQR$: Angles are $67^\circ$, $54^\circ$, and $59^\circ$.
• Triangle $STU$: Angles are $67^\circ$, $54^\circ$, and $59^\circ$.

Since the angles of the two triangles are the same, the triangles are similar by the Angle-Angle-Angle (AAA) similarity criterion.

Task 2

Now that we know the triangles are similar, we can set up a proportion to find $x$. We need to match the corresponding sides.

• Side $RQ$ corresponds to side $TS$
• Side $PQ$ corresponds to side $US$

So, we can set up the proportion:

$\frac{RQ}{TS} = \frac{PQ}{US}$

Plugging in the given values:

$\frac{37}{x} = \frac{40}{31}$

Task 3

Now, we solve for $x$:

$x = \frac{37 \cdot 31}{40}$

$x = \frac{1147}{40}$

$x = 28.675$

Rounding to the nearest tenth, we get:

$x \approx 28.7$

Answer:
$x \approx 28.7$

Okay, I see three problems and I have solved all of them for you.

Okay, I see three problems. I will solve all of them for you and present the solutions together.

Problem 1

Task 1: Check for Similarity

• Triangle $BCD$: Angles are $39^\circ$, $86^\circ$, and $55^\circ$.
• Triangle $EFG$: Angles are $39^\circ$, $86^\circ$, and $55^\circ$.

The triangles are similar by the AAA criterion.

Task 2: Set up Proportion

$\frac{BD}{EG} = \frac{BC}{EF}$

$\frac{97}{x} = \frac{61}{15}$

Task 3: Solve for $x$

$x = \frac{97 \cdot 15}{61}$

$x = \frac{1455}{61}$

$x \approx 23.852459$

Rounding to the nearest tenth:

$x \approx 23.9$

Answer: $x \approx 23.9$

Problem 2

Task 1: Check for Similarity

• Triangle $RST$: Angles are $49^\circ$, $57^\circ$, and $74^\circ$.
• Triangle $UVW$: Angles are $49^\circ$, $57^\circ$, and $74^\circ$.

The triangles are similar by the AAA criterion.

Task 2: Set up Proportion

$\frac{RS}{UV} = \frac{RT}{UW}$

$\frac{83}{37} = \frac{91}{x}$

Task 3: Solve for $x$

$x = \frac{91 \cdot 37}{83}$

$x = \frac{3367}{83}$

$x \approx 40.566265$

Rounding to the nearest tenth:

$x \approx 40.6$

Answer: $x \approx 40.6$

Problem 3

Task 1: Check for Similarity

• Triangle $PQR$: Angles are $67^\circ$, $54^\circ$, and $59^\circ$.
• Triangle $STU$: Angles are $67^\circ$, $54^\circ$, and $59^\circ$.

The triangles are similar by the AAA criterion.

Task 2: Set up Proportion

$\frac{RQ}{TS} = \frac{PQ}{US}$

$\frac{37}{x} = \frac{40}{31}$

Task 3: Solve for $x$

$x = \frac{37 \cdot 31}{40}$

$x = \frac{1147}{40}$

$x = 28.675$

Rounding to the nearest tenth:

$x \approx 28.7$

Answer: $x \approx 28.7$

## Задание 1

### Task 1: Check for Similarity

*   Triangle $GIH$: Angles are $55^\circ$, $50^\circ$, and $75^\circ$.
*   Triangle $LKJ$: Angles are $55^\circ$, $50^\circ$, and $75^\circ$.

The triangles are similar by the AAA criterion.

### Task 2: Set up Proportion

$\frac{GI}{LJ} = \frac{IH}{JK}$

$\frac{16}{54} = \frac{19}{x}$

### Task 3: Solve for $x$

$x = \frac{19 \cdot 54}{16}$

$x = \frac{1026}{16}$

$x = 64.125$

Rounding to the nearest tenth:

$x \approx 64.1$

**Answer:** $x \approx 64.1$