Lines And Angles
NIOS · Class 10 · Maths
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In the figure, two parallel lines are cut by a transversal. If one of the corresponding angles measures 65°, what is the measure of its corresponding angle?
Two complementary angles are in the ratio 2:3. Find the measure of the smaller angle.
In triangle ABC, if ∠A = 60° and ∠B = 70°, what is the measure of ∠C?
When two lines intersect, they form four angles. If one angle measures 115°, what is the measure of its vertically opposite angle?
Sample Questions
Two supplementary angles are in the ratio 4:5. Find the measure of the larger angle.
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100°
Step 1: Let the angles be 4x and 5x since they are in ratio 4:5. Step 2: Since they are supplementary, their sum equals 180°: 4x + 5x = 180°. Step 3: Simplify: 9x = 180°, so x = 20°. Step 4: The larger angle = 5x = 5(20°) = 100°. Step 5: Verify: 80° + 100° = 180° ✓
In triangle PQR, the exterior angle at vertex Q measures 120°. If ∠P = 50°, find ∠R.
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70°
Step 1: Use the exterior angle theorem - an exterior angle equals the sum of the two non-adjacent interior angles. Step 2: The exterior angle at Q = ∠P + ∠R. Step 3: Substitute: 120° = 50° + ∠R. Step 4: Solve: ∠R = 120° - 50° = 70°. Step 5: Verify using angle sum: ∠P + ∠Q + ∠R = 50° + 60° + 70° = 180° ✓
Two parallel lines are cut by a transversal. If one interior angle on the same side measures 75°, what is the measure of the other interior angle on the same side?
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105°
Step 1: Identify that we have co-interior angles (interior angles on the same side of the transversal). Step 2: Recall the property that co-interior angles are supplementary when lines are parallel. Step 3: Set up equation: 75° + other angle = 180°. Step 4: Solve: other angle = 180° - 75° = 105°. Step 5: This confirms the co-interior angle property.
In an isosceles triangle ABC where AB = AC, if the vertex angle ∠A = 40°, find each base angle.
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70°
Step 1: In isosceles triangle ABC with AB = AC, the base angles ∠B and ∠C are equal. Step 2: Apply angle sum property: ∠A + ∠B + ∠C = 180°. Step 3: Since ∠B = ∠C, we have: 40° + ∠B + ∠B = 180°. Step 4: Simplify: 40° + 2∠B = 180°. Step 5: Solve: 2∠B = 140°, so ∠B = 70°. Therefore, each base angle is 70°.
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