Question

1. the angle measures of a triangle are shown in the figure below.

triangle with angles 47°, 15 + x, and 18 + 4x
which two of the following equations could be used to find the value of x?
□ 15 + x + 18 + 4x + 47 = 90
□ 15 + x + 18 + 4x = 180 − 47
□ 15 + x + 47 = 18 + 4x
□ 15 + x + 18 + 4x + 47 = 180
□ 15 + x = 18 + 4x

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\). So, the three angles \(15 + x\), \(18 + 4x\), and \(47^\circ\) must add up to \(180^\circ\).

Step2: Analyze Each Equation

• First equation: \(15 + x + 18 + 4x + 47 = 90\) is wrong because the sum should be \(180\), not \(90\).
• Second equation: \(15 + x + 18 + 4x = 180 - 47\). Subtract \(47\) from both sides of \(15 + x + 18 + 4x + 47 = 180\), so this is correct.
• Third equation: \(15 + x + 47 = 18 + 4x\) assumes two angles sum to the third, which isn't a triangle angle property, so wrong.
• Fourth equation: \(15 + x + 18 + 4x + 47 = 180\) directly uses the angle - sum property, so correct.
• Fifth equation: \(15 + x = 18 + 4x\) assumes two angles are equal, no basis, so wrong.

Answer:

\(15 + x + 18 + 4x = 180 - 47\), \(15 + x + 18 + 4x + 47 = 180\)