Question

In the given figure, `Delta OQP~ Delta OAB, angle OPQ =56^(@) and angle BOQ=132^(@)`. Find `angleOAB`.

Answer 1

In `Delta OPQ`, we have
`angle BOQ= angle OPQ+angle OQP` [ `:.` the exterior angle is equal to the sum of the two interior opposite angles ]
`rArr angle OQP= angle BOQ- angle OPQ =132^(@)=132^(@)-56^(@)=76^(@)`,
Now, `Delta OQP~ Delta OAB`
`rArr angle OQP= angle OAB` [ corresponding angles of similar triangles]
`:. angleOAB= angle OQP=76^(@)`