Question

The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle. (6x+3)° (2x+7)° 90° Answer

Answer 1

To find the measure of the smallest angle in the triangle, we first need to establish an equation using the fact that the sum of the angles in a triangle is \(180^\circ\).

Given the angles are:
- \( (6x+3)^\circ \)
- \( (2x+7)^\circ \)
- \( 90^\circ \)

We can write the equation:

\[
(6x + 3) + (2x + 7) + 90 = 180
\]

Now, combine like terms:

\[
6x + 2x + 3 + 7 + 90 = 180
\]

This simplifies to:

\[
8x + 100 = 180
\]

Next, we solve for \(x\):

\[
8x = 180 - 100
\]
\[
8x = 80
\]
\[
x = 10
\]

Now that we have \(x\), we can find the measures of the angles:

1. \( (6x + 3)^\circ = 6(10) + 3 = 60 + 3 = 63^\circ \)
2. \( (2x + 7)^\circ = 2(10) + 7 = 20 + 7 = 27^\circ \)
3. \( 90^\circ \)

Now we compare the angles \( 63^\circ \), \( 27^\circ \), and \( 90^\circ \) to determine the smallest angle.

The smallest angle is:

\[
\boxed{27^\circ}
\]