2. In Fig. 6.40, 2X = 62°, _ XYZ = 54°. If YO and ZO are the bisectors of ZXYZ and ZXZY respectively of A XYZ, find Z OZY and Z YOZ.
Answers
In Fig. 6.40, 2X = 62°, _ XYZ = 54°. If YO and ZO are the bisectors of ZXYZ and ZXZY respectively of A XYZ, find Z OZY and Z YOZ.
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All necessary formulas⤵️
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Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof .Thus, the sum of the interior angles of a triangle is 180°.
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Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.Alternate interior angles are equal if the lines intersected by the transversal are parallel.
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The sum of 2 numbers
example
how to find "a" if a is not mentioned
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The sum of two numbers
example
how to find "a" if a is not mentioned
Given
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If there is a common ray between and so it is a adjacent angle.
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Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.
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Here 180°.
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In ∆XYZ,
Angle X = 62°
Angle XYZ = 54°
<X + <XYZ + <Z = 180° ... angle addition property of ∆
62° + 54° + <Z = 180°
116° + <z = 180°
<Z = 180° - 116°
<Z = 64°
OZ is angle bisector of angle XZY
Angle OZY = 32° ... 1
Similarly OY is angle bisector of angle XYZ
Angle OYZ = 27° ... 2
In triangle OYZ,
<OYZ + <OZY + <YOZ=180° ...angle sum property of ∆