Question

unit 2 - lesson 7: comprehension check b

1. in the figure, ( mangle1 = 89^{circ} ) and ( mangle2 = 82^{circ} )

what is ( mangle4 )?
a. ( 98^{circ} )
b. ( 121^{circ} )
c. ( 133^{circ} )
d. ( 141^{circ} )

1. determine whether each statement is true.

select true or false for each statement.

a triangle can have more than one right angle.	true	false
each vertex of a triangle has two exterior angles, and these angles are always congruent.	true	false
the sum of the measures of the interior angles of a triangle is the same as the sum of the exterior angles.	true	false
all the exterior angles of a triangle can be obtuse angles.	true	false

1. the figure shows a triangle with an exterior angle at each vertex.

what is the value of ( z )?
( z = )

Explanation:

Step1: Find the interior angles adjacent to the exterior angles

The interior angle adjacent to \(133^{\circ}\) is \(180 - 133=47^{\circ}\).
The interior angle adjacent to \(139^{\circ}\) is \(180 - 139 = 41^{\circ}\).

Step2: Use the sum of interior angles of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\).
Let the third interior angle be \(x\), then \(x+47 + 41=180\), so \(x = 180-(47 + 41)=92^{\circ}\).

Step3: Find the value of \(z\)

The angle \(z\) and the \(92^{\circ}\) interior angle are adjacent to a straight - line (sum to \(180^{\circ}\)).
So \(z=180 - 92=88^{\circ}\).

Answer:

\(z = 88^{\circ}\)