Question

determining an unknown angle measure
the measure of angle 1 is (3x + 10)° and the measure of what is the measure of angle 7?
angle 4 is (4x - 15)°
2 4 6 8
1 3 5 7
a c b

Explanation:

Step1: Use vertical - angle property

Since angle 1 and angle 4 are vertical angles, they are equal. So, $3x + 10=4x - 15$.

Step2: Solve for x

Subtract $3x$ from both sides: $10=x - 15$. Then add 15 to both sides, we get $x = 25$.

Step3: Find measure of angle 1

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

Step4: Use corresponding - angle property

Angle 1 and angle 5 are corresponding angles, so angle 5 = angle 1 = $85^{\circ}$. Angle 5 and angle 7 are supplementary (linear - pair), so angle 7=$180^{\circ}-$angle 5.

Step5: Calculate measure of angle 7

angle 7=$180 - 85=95^{\circ}$.

Answer:

$95$