Question

find the value of \\( \angle 1 \\).
1
\\( 76 ^ { \circ } \\)
1
\\( 59 ^ { \circ } \\)
a \\( 17 ^ { \circ } \\)
b \\( 135 ^ { \circ } \\)
c \\( 45 ^ { \circ } \\)
d \\( 104 ^ { \circ } \\)

Explanation:

Step1: Recall the triangle angle - sum formula

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 76^{\circ}\), \(B=59^{\circ}\), and \(C = \angle1\). Then \(A + B + C=180^{\circ}\).

Step2: Solve for \(\angle1\)

Substitute the values of \(A\) and \(B\) into the formula: \(\angle1=180^{\circ}-(76^{\circ}+59^{\circ})\). First, calculate \(76^{\circ}+59^{\circ}=135^{\circ}\). Then \(\angle1 = 180^{\circ}-135^{\circ}\).

Answer:

\(45^{\circ}\), so the answer is C.