7. One of the exterior angles of a triangle is 100°. The interior opposite angles are equal to each other. Find the measure of these equal interior opposite angles. 8. One of the exterior angles of a triangle is 115º and the interior opposite angles are in the ratio 2:3. Find the magnitudes of interior opposite angles 9. An exterior angle is 104 and the interior opposite angles differ by 10°. Find all the angles of the triangle 10. One of the interior opposite angles is 60°. If the sum of another interior opposite angle and the exterior angle is 180°, find the magnitudes of unknown interior opposite angle and the exterior angle. 11. If the two interior opposite angles of an exterior angle are complementary, then what is the measure of the exterior angle? Also, write the type of a triangle 12. In the given figure, PQR = 90°, SQ 1 PR and PQS = 60°, find the angles x and y.
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Step-by-step explanation:
Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.
Let ΔABC be a triangle where the side BC is produced.
By the theorem we have
∠A+∠B=100
o
…………..(1)
It is given that the interior opposite angles are equal i.e., ∠A=∠B.
∴ Equation (1) becomes
2∠A=100
o
⇒∠A=50
o
⇒∠B=50
o
Using angle sum property of a triangle,
Sum of all angles of a triangle =180
o
⇒∠A+∠B+∠C=180
o
⇒100+∠C=180
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[from (1)]
⇒∠C=180
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−100
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⇒∠C=80
o
.
Hence ∠A=50
o
∠B=50
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∠C=80
o
.
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