Question

1. here is a diagram of triangle lmn. a. find the measures of angles a, b, and c. b. find the sum of the measures of angles a, b, and c. c. what do you notice about these three angles?

Explanation:

Step1: Find angle a

An angle and its exterior - angle are supplementary. So, $a = 180^{\circ}-34^{\circ}=146^{\circ}$.

Step2: Find angle b

Similarly, $b = 180^{\circ}-61^{\circ}=119^{\circ}$.

Step3: Find the third - interior angle of the triangle

The sum of interior angles of a triangle is $180^{\circ}$. Let the third - interior angle of $\triangle LMN$ be $x$. Then $x=180^{\circ}-(34^{\circ}+61^{\circ}) = 85^{\circ}$.

Step4: Find angle c

Since $x$ and $c$ are supplementary, $c = 180^{\circ}-85^{\circ}=95^{\circ}$.

Step5: Find the sum of a, b, and c

$a + b + c=146^{\circ}+119^{\circ}+95^{\circ}=360^{\circ}$.

Answer:

a. $a = 146^{\circ}$, $b = 119^{\circ}$, $c = 95^{\circ}$
b. $360^{\circ}$
c. The sum of the exterior angles of a triangle is $360^{\circ}$.