Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 19, 2024

Find the value of $k$ where the interior angles of a triangle are $k^{\circ}, 27^{\circ}$ , and $10^{\circ}$ . $k=\square^{\circ}$

STEP 1

Assumptions
1. The sum of the interior angles of a triangle is always $180^{\circ}$ .
2. The triangle has three interior angles with measures $k^{\circ}, 27^{\circ}$ , and $10^{\circ}$ .

STEP 2

To find the value of $k$ , we will use the fact that the sum of the interior angles of a triangle is $180^{\circ}$ .
$k^{\circ} + 27^{\circ} + 10^{\circ} = 180^{\circ}$

STEP 3

Combine the known angle measures to simplify the equation.
$k^{\circ} + 37^{\circ} = 180^{\circ}$

STEP 4

Subtract $37^{\circ}$ from both sides of the equation to solve for $k^{\circ}$ .
$k^{\circ} = 180^{\circ} - 37^{\circ}$

STEP 5

Calculate the value of $k^{\circ}$ .
$k^{\circ} = 143^{\circ}$
The value of $k$ is $143^{\circ}$ .

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