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P, Q & R form a right-angled triangle.
R, S & P lie on a straight line.
PS = SQ and
∠
SQR = 46°.
Work out
∠
RPQ

P Q Amp R Form A Rightangled Triangle R S Amp P Lie On A Straight Line PS SQ And SQR 46 Work Out RPQ class=

Sagot :

akposevictor

Answer:

m<RPQ = 22°

Step-by-step explanation:

Given:

m<SRQ = 90°

PS = PQ

m<SQR = 46°

Required:

m<RPQ

Solution:

m<SQR + m<SRQ + m<RSQ = 180°

Substitute

46° + 90° + m<RSQ = 180°

m<RSQ = 180° - 136°

m<RSQ = 44°

Find m<PSQ:

m<PSQ = 180° - m<RSQ (Angles on a straight line

m<PSQ = 180° - 44° (Substitution)

m<PSQ = 136°

Find m<RPQ:

∆QSP is an isosceles triangle with two equal base angles. Therefore:

m<RPQ = ½(180° - 136°)

m<RPQ = 22°

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