Question

In ΔABC, M and N are midpoints of AB and AC. ∠AMN = 3x – 25, ∠B = 2x + 5.
∴ The value of x is:

पर्याय

• 40°

• 30°

• 25°

• 35°

Answer 1

30°

Explanation:

We are given a triangle ΔABC where M and N are the midpoints of sides AB and AC, respectively.

We are also given the following angles:

• ∠AMN = 3x – 25
• ∠B = 2x + 5

Step 1: Use the properties of the midpoint theorem

The line segment MN joining the midpoints of AB and AC is parallel to side BC (by the Midpoint | Theorem) and its length is half the length of BC.

Also, since MN || BC, the angles ∠AMN and ∠ABC are equal.

Therefore, we can set up the equation ∠AMN = ∠ABC.

Step 2: Set up the equation

We know that:

• ∠AMN = 3x – 25
• ∠ABC = 2x + 5

Since ∠AMN = ∠ABC, we can equate these two expressions:

3x – 25 = 2x + 5

Step 3: Solve for x

Now, we solve the equation for x:

3x – 2x = 5 + 25

x = 30