Question

9/9 triangle angle sum theorem
your turn!
multiple-choice question
what is the measure of the missing angle in question 1?
options: 180, 90, 130, 58

Explanation:

Step1: Recall Triangle Angle Sum Theorem

The sum of the interior angles of a triangle is \( 180^\circ \). Let the two given angles be \( 45^\circ \) and \( 77^\circ \), and the missing angle be \( x \).

Step2: Set up the equation

Using the theorem, we have \( 45^\circ + 77^\circ + x = 180^\circ \).

Step3: Calculate the sum of given angles

First, find the sum of \( 45^\circ \) and \( 77^\circ \): \( 45 + 77 = 122 \), so \( 45^\circ + 77^\circ = 122^\circ \).

Step4: Solve for \( x \)

Substitute into the equation: \( 122^\circ + x = 180^\circ \). Then, \( x = 180^\circ - 122^\circ = 58^\circ \).

Answer:

58 (corresponding to the option with 58, assuming the options are labeled with the angle measure, e.g., the last option with 58)