The value of [tex]\angle{k}[/tex] is [tex]\fbox{\begin\\\ \bf 73^{\circ}\\\end{minispace}}[/tex].
Further explanation:
Consider, the given triangle as [tex]\triangle{ABC}[/tex] shown in figure 1.
Now, the value of [tex]\angle{A}[/tex] is 62 degree, the value of [tex]\angle{B}[/tex] is 45 degree and the value of [tex]\angle{C}[/tex] is [tex]k[/tex] .
From the property of the triangle, we know that sum of angles of a triangle is equal to 180 degree.
Now, for [tex]\triangle{ABC}[/tex] it can be written as follows:
[tex]A+B+C=180[/tex] ……(1)
Substitute 62 for [tex]A[/tex], 45 for [tex]B[/tex] and [tex]k[/tex] for [tex]C[/tex] in equation (1) to obtain the value of [tex]k[/tex].
[tex]\begin{aligned}62+45+k&=180\\107+k&=180\\k&=180-107\\k&=73\end{aligned}[/tex]
Thus, the value of angle [tex]k[/tex] is [tex]\fbox{\begin\\\ \bf 73^{\circ}\\\end{minispace}}[/tex].
Learn more:
1. Which rule describes the transformation? https://brainly.com/question/2992432
2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797
3. Look at the figure, which trigonometric ratio should you use to find x? https://brainly.com/question/9880052
Answer Details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangle
Keywords: triangle, similar, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, triangle ABC.
