AXYZ and A PYZ are two isosceles triangle on the same base YZ with XY=XZ and PY=PZ. If <P=110° and <XYP-30-,then find <YXZ
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<YXZ = 50°
Explanation:
Given:
<P = 110°
<XYP = 30° then,
<XZP = 30°
Solve:
Let <PYZ and <PZY be x.
So,
110° + x + x = 180° [Sum of angle of a triangle is 180°]
=> 110° + 2x = 180°
=> 2x = 180° - 110°
=> 2x = 70°
=> x = 35°
Hence, <PYZ = x = 35° and <PZY = x = 35°
Then,
<XYZ + <YZX + <YXZ = 180° [Sum of angle of a triangle is 180°]
(<XYP+<PYZ)+(<XZP+<PZY)+<YXZ = 180°
=> (30° + 35°) + (30° + 35°) + <YXZ = 180°
=> 65° + 65° + <YXZ = 180°
=> 130° + <YXZ = 180°
=> <YXZ = 180° - 130° = 50°
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