Question

the lounge chair has different settings that change the angles formed by its parts. suppose ( mangle2 = 32 ) and ( mangle3 = 81 ). find ( mangle1 ), the angle formed by the back of the chair and the arm rest.

1. the lid of a grand piano is held open by a prop stick whose length can vary, depending upon the effect desired. the longest prop stick makes angles as shown. what are the values of ( x ) and ( y )?

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the triangle formed by the angles \( \angle1\), \( \angle2\), and \( \angle3\) (where \( \angle3\) is the exterior angle), we have the formula \( m\angle3=m\angle1 + m\angle2\).

Step2: Solve for \( m\angle1\)

Rearrange the formula from Step1 to isolate \( m\angle1\). We get \( m\angle1=m\angle3 - m\angle2\).
Substitute \( m\angle2 = 32\) and \( m\angle3=81\) into the formula: \( m\angle1=81 - 32\).

$$m\angle1 = 49$$

Answer:

\( m\angle1 = 49\)