Question

ws interior and exterior angles of triangles revised.pdf
name ____ date __ period ____
find the value of x
(then the triangle diagrams with angles and x to solve)

Explanation:

Step1: Identify the problem type

This is a problem about interior and exterior angles of triangles, which falls under Geometry (a subfield of Mathematics). We'll solve one of the problems, say problem 1 (the first triangle with angles 75°, 42°, and x°).

Step2: Recall the triangle angle sum theorem

The sum of the interior angles of a triangle is \( 180^\circ \). So, for a triangle with angles \( a \), \( b \), and \( c \), \( a + b + c = 180^\circ \).

Step3: Apply the theorem to problem 1

Here, \( a = 75^\circ \), \( b = 42^\circ \), and \( c = x^\circ \). So, \( 75 + 42 + x = 180 \).

Step4: Solve for x

First, add 75 and 42: \( 75 + 42 = 117 \). Then, \( 117 + x = 180 \). Subtract 117 from both sides: \( x = 180 - 117 = 63 \).

Answer:

For problem 1 (the first triangle), \( x = 63^\circ \)