Triangle Angle Sum

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Show your work for each problem.

1.
What is the sum of all interior angles in any triangle?
1. a) $270°$
2. b) $360°$
3. c) $180°$
4. d) $90°$
2.
A triangle has angles of $50°$ and $70°$ . What is the third angle?
3.
In an equilateral triangle, all three angles are equal. What is the measure of each angle?
1. a) $90°$
2. b) $120°$
3. c) $45°$
4. d) $60°$
4.
A triangle has angles of $80°$ , $55°$ , and an unknown angle $x$ . Find $x$ .
5.
In a right triangle, one acute angle is $25°$ . What is the other acute angle?
6.
An isosceles triangle has two equal angles of $70°$ each. Find the third angle.
7.
A triangle has angles of $35°$ , $95°$ , and $x$ . What type of angle is $x$ ?
1. a)Acute ( $30°$ )
2. b)Acute ( $50°$ )
3. c)Right ( $90°$ )
4. d)Obtuse ( $130°$ )
8.
The angles of a triangle are in the ratio $2:3:4$ . What is the largest angle, in degrees?
9.
In a triangle, one angle is twice another, and the third angle is $30°$ . Find all three angles.
10.
Can a triangle have angles of $60°$ , $70°$ , and $60°$ ?
1. a)Yes, they sum to $180°$
2. b)No, a triangle cannot have two equal angles
3. c)No, they sum to $170°$
4. d)No, they sum to $190°$
11.
In a triangle, one angle is $20°$ more than another. The third angle is $80°$ . Find the smallest angle.
12.
In a triangle, the angles are $(2x + 10)°$ , $(3x - 20)°$ , and $(x + 40)°$ . Find the value of $x$ and all three angles.
13.
Why can't a triangle have two obtuse angles?
1. a)Every triangle needs at least one right angle
2. b)Obtuse angles are not allowed in triangles
3. c)Two obtuse angles would sum to more than $180°$
4. d)Triangles can only have acute angles
14.
An isosceles triangle has a vertex angle of $46°$ . What is each base angle?
15.
In a right triangle, one acute angle is $10°$ less than three times the other. Find both acute angles.
16.
An exterior angle of a triangle measures $130°$ . The two non-adjacent interior angles are in the ratio $2:3$ . Find all three interior angles.