Question

question image: a triangle with angles 70°, 65°, and one angle labeled ( x + 53 ). solve for ( x ).

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(70^\circ + 65^\circ + (x + 53)^\circ = 180^\circ\).

Step2: Simplify the left side

Calculate \(70 + 65 + 53 = 188\), so the equation becomes \(x + 188 = 180\).

Step3: Solve for x

Subtract 188 from both sides: \(x = 180 - 188 = -8\)? Wait, no, wait. Wait, \(70 + 65 = 135\), then \(135 + x + 53 = 180\). So \(x + 188 = 180\)? No, \(135 + 53 = 188\)? Wait, no, \(70 + 65 = 135\), then \(135 + (x + 53) = 180\). So \(x + 53 = 180 - 135 = 45\). Then \(x = 45 - 53 = -8\)? That can't be right. Wait, maybe I misread the triangle. Wait, maybe the sides? No, the labels are angles. Wait, maybe the third angle is \(x + 53\) degrees. So sum of angles: \(70 + 65 + (x + 53) = 180\). Let's recalculate: \(70 + 65 = 135\), \(135 + 53 = 188\), so \(x + 188 = 180\), so \(x = 180 - 188 = -8\). But angle can't be negative? Wait, maybe the problem is a typo, or maybe I misread the numbers. Wait, maybe the angles are 70, 65, and the third angle is \(x + 53\). Wait, 70 + 65 = 135, 180 - 135 = 45. So \(x + 53 = 45\), so \(x = 45 - 53 = -8\). Hmm. Maybe the original problem has different numbers? Wait, maybe I made a mistake. Let's check again. Sum of angles in triangle: 180. So 70 + 65 + (x + 53) = 180. Combine like terms: (70 + 65 + 53) + x = 180. 70 + 65 is 135, 135 + 53 is 188. So 188 + x = 180. Subtract 188: x = 180 - 188 = -8. So the answer is -8.

Answer:

\(x = -8\)