Question

33
solve for x

a) 36
b) 86
c) 77
d) 76

34
solve for x

a) 65
b) 60
c) 40
d) 120

35
which of the following terms best describes angle d?

a) exterior angle
b) remote interior angle
c) interior angle
d) corresponding angle

36
which is the correct set up to solve for x?

a) tan37 = x/12
b) sin37 = 12/x
c) cos37 = 12/x
d) sin37 = x/12

37
triangle sum theorem
∠1 + ∠2 + ∠3 = ____
the triangle sum theorem states that...

a) congruent angles
b) 90
c) 4
d) 180

Explanation:

Problem 33: Solve for \( x \)

Step 1: Recall the Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \( EFG \), the exterior angle at \( G \) (which is \( x \)) is equal to the sum of the two remote interior angles \( \angle E \) and \( \angle F \).
So, \( x=\angle E+\angle F \)

Step 2: Substitute the given angle measures

We know that \( \angle E = 28^{\circ} \) and \( \angle F=58^{\circ} \). Then \( x = 28^{\circ}+58^{\circ}=86^{\circ} \)

Step 1: Identify the angle relationship

We have a right - triangle \( SUT \) with a straight line at \( S \). The angle on the straight line is \( 150^{\circ} \), so the adjacent angle inside the triangle (at \( S \)) is \( 180^{\circ}- 150^{\circ}=30^{\circ} \)

Step 2: Use the Triangle Angle Sum Theorem

In a right - triangle, the sum of the interior angles is \( 180^{\circ} \). One angle is \( 90^{\circ} \) (right angle), one angle is \( 30^{\circ} \), and the third angle is \( x \). So, \( x + 90^{\circ}+30^{\circ}=180^{\circ} \)

Step 3: Solve for \( x \)

\( x=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ} \)

Step 1: Recall the definition of an exterior angle

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. In the given triangle, angle \( d \) is formed by side \( c \) and the extension of side \( d \) (the side of the triangle), so it is an exterior angle.

Answer:

b) 86

Problem 34: Solve for \( x \)