Question

unit 4: the angle sum of a triangle
question 1 find the value of each pronumeral.
question 2 find the value of each pronumeral.
question 3 find the value of each pronumeral.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for unknown angles in each triangle

For example, in a triangle with angles \(A\), \(B\), and \(C\), if \(A = a\), \(B = b\), and \(C=x\) (the unknown angle), then \(x=180-(a + b)\).

Let's take some examples from the questions:

• In the first triangle of Question 1 (a) with angles 50° and 85°, let the unknown angle be \(m\).
• First, find the sum of the known angles: \(50 + 85=135\).
• Then, \(m = 180-135 = 45\).
• In the first triangle of Question 2 (a) with angles 40° and 70°, let the unknown angle be \(x\).
• The sum of the known angles is \(40+70 = 110\).
• So, \(x=180 - 110=70\).

Answer:

The values of the pronumerals are found by subtracting the sum of the given angles in each triangle from 180°. For a complete set of answers, each triangle needs to be evaluated one - by - one using the formula \(x = 180-(a + b)\) where \(a\) and \(b\) are the given angles and \(x\) is the unknown angle.