Mathematics
Grade9
Easy
Question
The measure of the missing angle is
- 87°
- 82°
- 83°
- 72°
Hint:
Find the interior angle 2 nd triangle by using the exterior angle property. Also know the value of required angle by using sum of angles in a triangle property.
The correct answer is: 82°
Let x and y be the unknown angles of second triangle .
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
30°+80° = 66° + X°
X° = 110-66 = 44°
In the second triangle ,
X° + Y° + 54° = 180° (sum of angles in a triangle)
substitute x = 44° Then, Y ° = 180° - 54° - 44° = 180° - 98° = 82°
Therefore, The unknown angle is 82° .
¶A triangle has three angles or sides, and the sum of the angles or sides is always 180 degrees, the missing angle in the triangle's measurement is found by first taking the sum of the other two angles and then subtracting that number from 180.
Exterior Angle of Triangle Properties
The exterior angles of a triangle have three fundamental properties.
• In a triangle, every exterior angle and corresponding interior angle create a linear pair of angles. So, the interior and exterior angles add up to 180°.
• A triangle's exterior angle equals the sum of its two opposite interior angles (remote interior angles). The Exterior Angle Theorem is another name for this.
• The sum of the exterior angle of a triangle is 360°.
¶
Exterior Angle of Triangle Properties
The exterior angles of a triangle have three fundamental properties.
• In a triangle, every exterior angle and corresponding interior angle create a linear pair of angles. So, the interior and exterior angles add up to 180°.
• A triangle's exterior angle equals the sum of its two opposite interior angles (remote interior angles). The Exterior Angle Theorem is another name for this.
• The sum of the exterior angle of a triangle is 360°.
¶
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