Question

determining an unknown angle measure
the measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x - 15)°.
what is the measure of angle 7?
°

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Angle 1 and angle 4 are supplementary (they form a linear - pair). So, \((3x + 10)+(4x-15)=180\).

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Step2: Find the measure of angle 1

Substitute \(x = 25\) into the expression for angle 1: \(3x+10=3\times25 + 10=75 + 10=85^{\circ}\)

Step3: Use the property of corresponding angles

Angle 1 and angle 5 are corresponding angles. So, \(\angle1=\angle5 = 85^{\circ}\)

Step4: Use the property of vertical angles

Angle 5 and angle 7 are vertical angles. So, \(\angle7=\angle5\)

Answer:

\(85\)