Question

calculate the value of 'a' in the given figure

Answer 1

$\boxed{\boxed{\mathbf{\angle a = 149}}}$

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We know that,

$\mathsf{\angle P(exterior) = 62}$⁰

$\mathsf{PQ = PR}$

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Now,

$\mathsf{\angle P(exterior) = \angle PQR + \angle PRQ ----(1)}$

[∵ Exterior Angle of a Triangle = Sum of Interior Opposite angles of the Triangle(Exterior Angle Propetry)]

Also,

$\mathsf{\angle PQR = \angle PRQ ----(2)}$

[∵ Since, Angles opposite to Equal sides of Triangle are Equal]

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Now, From (1), We get

$\mathsf{=> \angle PRQ + \angle PRQ = 62}$

$\mathsf{=> 2 \angle PRQ = 62}$ [From (2)]

$\mathsf{\angle PRQ = \frac{62}{2}}\\ \boxed{\mathsf{\angle PRQ = 31}}$

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Now,

$\mathsf{\angle PRQ + \angle a = 180}$ [∵ A ray standing on a line forms supplementary anngles]

$\mathsf{=> 31 + \angle a = 180}\\\mathsf{=> \angle a = 180 - 31}\\ \\=> \boxed{\large\mathbf{\angle a = 149}}$