Question

solve the 13 question with equation.....

Answer 1

(i) In triangle PTQ,
= angle TPQ + angle PTQ + angle PQT = 180° ( sum of all angles of a triangle is 180°)
= 90° + angle PTQ + 20° = 180°
= 110° + angle PTQ = 180°
= angle PTQ = 180° - 110°
Therefore, angle PTQ = 70°;

(ii) = angle STU + angle QTU + angle PTQ = 180° (linear pair)
= 45° + angle QTU + 70° = 180° ( eq.1 )
= 115° + angle QTU = 180°
= angle QTU = 180° - 115°
Therefore, angle QTU = 65°;

(iii) In triangle STU,
= angle STU + angle SUT + angle UST = 180° ( Sum of all angles of a triangle is 180°)
= 45° + angle SUT + 90° = 180°
= 135° + angle SUT = 180°
= Therefore, angle SUT = 180° - 135° = 45°;

(iv) = angle SUT + angle RUQ + angle TUQ = 180° (linear pair)
= 45° + angle RUQ + 70° = 180°
= 115° + angle RUQ = 180°
= Therefore, angle RUQ = 180° - 115° = 65°;

(v) In triangle RQU,
= angle RUQ + angle RQU + angle URQ = 180° (Sum of all angles of a triangle is 180°)
= 65° + angle RQU + 90° = 180°
= 155° + angle RQU = 180°
= Therefore, angle RQU = 180° - 155° = 25°;

(vi) In triangle QTU,
= angle QUT + angle QTU + angle UQT = 180° ( Sum of all angles of a triangle is 180° )
= 70° + 65° + angle UQT = 180°
= 135° + angle UQT = 180°
= Therefore, angle UQT = 180° - 135° = 45°...


Solved...

Answer 2

angle UQT=45 degree

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