Question

1. tailoring each lapel on a suit jacket is in the shape of a triangle. two of the three angles of each triangle measure 47° and 68°. what is the measure of the third angle?

1. flags a naval distress signal flag is in the shape of a triangle. two of the three angles measure 55° each. what is the measure of the third angle?

1. carpentry the supports of a wooden table are in the shape of a triangle. find the angles of the triangle if the measures of the angles are in the ratio 4x : 4x : 10x.

1. maps the three towns of ripon, sparta, and walker form a triangle as shown below. what is the value of x in the triangle?

1. hiking the figure shows the oak creek trail, which is shaped like a triangle. what is the value of x in the figure?

1. ladder the figure shows a ladder leaning against a wall, forming a triangle. what is the value of x in the figure?

Explanation:

Problem 1:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let the third angle be \(x\).

Step2: Set up the equation

\(47^\circ + 68^\circ + x = 180^\circ\)

Step3: Solve for \(x\)

First, calculate \(47 + 68 = 115\). Then, \(x = 180 - 115 = 65\).

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let the third angle be \(x\).

Step2: Set up the equation

\(55^\circ + 55^\circ + x = 180^\circ\)

Step3: Solve for \(x\)

First, calculate \(55 + 55 = 110\). Then, \(x = 180 - 110 = 70\).

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). The angles are in the ratio \(4x:4x:10x\).

Step2: Set up the equation

\(4x + 4x + 10x = 180\)

Step3: Combine like terms

\(18x = 180\)

Step4: Solve for \(x\)

\(x = \frac{180}{18} = 10\)

Step5: Find each angle

First angle: \(4x = 4\times10 = 40^\circ\), Second angle: \(4x = 40^\circ\), Third angle: \(10x = 10\times10 = 100^\circ\)

Answer:

\(65^\circ\)

Problem 2: