Question

If an angle, BGC equals 16 X -4 and angle CGD equals 2X +13. Find the value of X so that angle BGD is a right angle.

Answer 1

To find the value of \( X \) such that angle \( BGD \) is a right angle, we need to first express angle \( BGD \) in terms of the angles \( BGC \) and \( CGD \).

Given:
- Angle \( BGC = 16X - 4 \)
- Angle \( CGD = 2X + 13 \)

Since angle \( BGD \) is the external angle at point \( G \), we know:
\[
\text{angle } BGD = \text{angle } BGC + \text{angle } CGD
\]

Substituting the expressions for the angles:
\[
\text{angle } BGD = (16X - 4) + (2X + 13)
\]
\[
\text{angle } BGD = 16X - 4 + 2X + 13
\]
\[
\text{angle } BGD = 18X + 9
\]

For angle \( BGD \) to be a right angle, it must equal \( 90^\circ \):
\[
18X + 9 = 90
\]

Now, we will solve for \( X \):
1. Subtract 9 from both sides:
\[
18X = 90 - 9
\]
\[
18X = 81
\]

2. Divide by 18:
\[
X = \frac{81}{18}
\]
\[
X = 4.5
\]

Thus, the value of \( X \) that makes angle \( BGD \) a right angle is \( \boxed{4.5} \).